A367587 -id:A367587 - cp's OEIS frontend

A367579 Irregular triangle read by rows where row n is the multiset multiplicity kernel (MMK) of the multiset of prime indices of n.

1, 2, 1, 3, 1, 1, 4, 1, 2, 1, 1, 5, 1, 2, 6, 1, 1, 2, 2, 1, 7, 1, 2, 8, 1, 3, 2, 2, 1, 1, 9, 1, 2, 3, 1, 1, 2, 1, 4, 10, 1, 1, 1, 11, 1, 2, 2, 1, 1, 3, 3, 1, 1, 12, 1, 1, 2, 2, 1, 3, 13, 1, 1, 1, 14, 1, 5, 2, 3, 1, 1, 15, 1, 2, 4, 1, 3, 2, 2, 1, 6, 16, 1, 2

Offset: 1

Gus Wiseman, Nov 25 2023

Row n = 1 is empty.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
We define the multiset multiplicity kernel MMK(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then min(S) has multiplicity |S| in MMK(m). For example, MMK({1,1,2,2,3,4,5}) = {1,1,3,3,3}, and MMK({1,2,3,4,5,5,5,5}) = {1,1,1,1,5}.
Note: I chose the word 'kernel' because, as with A007947 and A304038, MMK(m) is constructed using the same underlying elements as m and has length equal to the number of distinct elements of m. However, it is not necessarily a submultiset of m.

			The first 45 rows:
     1: {}      16: {1}       31: {11}
     2: {1}     17: {7}       32: {1}
     3: {2}     18: {1,2}     33: {2,2}
     4: {1}     19: {8}       34: {1,1}
     5: {3}     20: {1,3}     35: {3,3}
     6: {1,1}   21: {2,2}     36: {1,1}
     7: {4}     22: {1,1}     37: {12}
     8: {1}     23: {9}       38: {1,1}
     9: {2}     24: {1,2}     39: {2,2}
    10: {1,1}   25: {3}       40: {1,3}
    11: {5}     26: {1,1}     41: {13}
    12: {1,2}   27: {2}       42: {1,1,1}
    13: {6}     28: {1,4}     43: {14}
    14: {1,1}   29: {10}      44: {1,5}
    15: {2,2}   30: {1,1,1}   45: {2,3}

Indices of empty and singleton rows are A000961.
Row lengths are A001221.
Depends only on rootless base A052410, see A007916.
Row minima are A055396.
Rows have A071625 distinct elements.
Indices of constant rows are A072774.
Indices of strict rows are A130091.
Rows have Heinz numbers A367580.
Row sums are A367581.
Row maxima are A367583, opposite A367587.
Index of first row with Heinz number n is A367584.
Sorted row indices of first appearances are A367585.
Indices of rows of the form {1,1,...} are A367586.
Agrees with sorted prime signature at A367683, counted by A367682.
A submultiset of prime indices at A367685, counted by A367684.
A007947 gives squarefree kernel.
A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
A124010 lists prime multiplicities (prime signature), sorted A118914.
A181819 gives prime shadow, with an inverse A181821.
A238747 gives prime metasignature, reversed A353742.
A304038 lists distinct prime indices, length A001221, sum A066328.
A367582 counts partitions by sum of multiset multiplicity kernel.
Cf. A000720, A001597, A005117, A027746, A027748, A051904, A052409, A061395, A062770, A175781, A288636, A289023.

mmk[q_]:=With[{mts=Length/@Split[q]}, Sort[Table[Min@@Select[q,Count[q,#]==i&], {i,mts}]]];
Table[mmk[PrimePi/@Join@@ConstantArray@@@If[n==1, {},FactorInteger[n]]], {n,100}]

For all positive integers n and k, row n^k is the same as row n.

A367581 Sum of the multiset multiplicity kernel (in which each multiplicity becomes the least element of that multiplicity) of the prime indices of n.

Original entry on oeis.org

0, 1, 2, 1, 3, 2, 4, 1, 2, 2, 5, 3, 6, 2, 4, 1, 7, 3, 8, 4, 4, 2, 9, 3, 3, 2, 2, 5, 10, 3, 11, 1, 4, 2, 6, 2, 12, 2, 4, 4, 13, 3, 14, 6, 5, 2, 15, 3, 4, 4, 4, 7, 16, 3, 6, 5, 4, 2, 17, 5, 18, 2, 6, 1, 6, 3, 19, 8, 4, 3, 20, 3, 21, 2, 5, 9, 8, 3, 22, 4, 2, 2

Offset: 1

Gus Wiseman, Nov 28 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

We define the multiset multiplicity kernel MMK(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then min(S) has multiplicity |S| in MMK(m). For example, MMK({1,1,2,2,3,4,5}) = {1,1,3,3,3}, and MMK({1,2,3,4,5,5,5,5}) = {1,1,1,1,5}. As an operation on multisets, MMK is represented by A367579, and as an operation on their Heinz numbers, it is represented by A367580.

			The multiset multiplicity kernel of {1,2,2,3} is {1,1,2}, so a(90) = 4.

Positions of 1's are A000079 without 1.
Positions of first appearances are A008578.
Depends only on rootless base A052410, see A007916, A052409.
The triangle A367579 has these as row sums, ranks A367580.
The triangle for this rank statistic is A367582.
For maximum instead of sum we have A367583, opposite A367587.
A007947 gives squarefree kernel.
A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
A124010 gives prime signature, sorted A118914.
A181819 gives prime shadow, with an inverse A181821.
A238747 gives prime metasignature, reverse A353742.
A304038 lists distinct prime indices, length A001221, sum A066328.
Cf. A000720, A005117, A051904, A055396, A061395, A071625, A072774, A130091, A175781, A367584, A367585.

mmk[q_]:=With[{mts=Length/@Split[q]}, Sort[Table[Min@@Select[q,Count[q,#]==i&], {i,mts}]]];
Table[Total[mmk[PrimePi/@Join@@ConstantArray@@@FactorInteger[n]]], {n,100}]

a(n^k) = a(n) for all positive integers n and k.
a(n) = A056239(A367580(n)).
If n is squarefree, a(n) = A055396(n)*A001222(n).

A367583 Greatest element in row n of A367579 (multiset multiplicity kernel).

Original entry on oeis.org

0, 1, 2, 1, 3, 1, 4, 1, 2, 1, 5, 2, 6, 1, 2, 1, 7, 2, 8, 3, 2, 1, 9, 2, 3, 1, 2, 4, 10, 1, 11, 1, 2, 1, 3, 1, 12, 1, 2, 3, 13, 1, 14, 5, 3, 1, 15, 2, 4, 3, 2, 6, 16, 2, 3, 4, 2, 1, 17, 2, 18, 1, 4, 1, 3, 1, 19, 7, 2, 1, 20, 2, 21, 1, 3, 8, 4, 1, 22, 3, 2, 1

Offset: 1

Gus Wiseman, Nov 28 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

We define the multiset multiplicity kernel MMK(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then min(S) has multiplicity |S| in MMK(m). For example, MMK({1,1,2,2,3,4,5}) = {1,1,3,3,3}, and MMK({1,2,3,4,5,5,5,5}) = {1,1,1,1,5}.

			For 450 = 2^1 * 3^2 * 5^2, we have MMK({1,2,2,3,3}) = {1,2,2} so a(450) = 2.

Positions of first appearances are A008578.
Depends only on rootless base A052410, see A007916, A052409.
For minimum instead of maximum element we have A055396.
Row maxima of A367579.
Greatest prime index of A367580.
Positions of 1's are A367586 (powers of even squarefree numbers).
The opposite version is A367587.
A007947 gives squarefree kernel.
A072774 lists powers of squarefree numbers.
A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
A124010 gives prime signature, sorted A118914.
A181819 gives prime shadow, with an inverse A181821.
A238747 gives prime metasignature, reverse A353742.
A304038 lists distinct prime indices, length A001221, sum A066328.
A363486 gives least prime index of greatest exponent.
A363487 gives greatest prime index of greatest exponent.
A364191 gives least prime index of least exponent.
A364192 gives greatest prime index of least exponent.
Cf. A000720, A000961, A051904, A061395, A071625, A130091, A289023, A367581, A367584, A367585, A367683.

mmk[q_]:=With[{mts=Length/@Split[q]},Sort[Table[Min@@Select[q,Count[q,#]==i&],{i,mts}]]];
Table[If[n==1,0,Max@@mmk[PrimePi/@Join@@ConstantArray@@@If[n==1,{},FactorInteger[n]]]],{n,1,100}]

a(n) = A061395(A367580(n)).
a(n^k) = a(n) for all positive integers n and k.
If n is a power of a squarefree number, a(n) = A055396(n).

A367586 Numbers whose prime indices have a multiset multiplicity kernel (in which each prime exponent becomes the least prime factor with that exponent) that is all ones {1,1,...}. Positions of powers of 2 in A367580.

Original entry on oeis.org

1, 2, 4, 6, 8, 10, 14, 16, 22, 26, 30, 32, 34, 36, 38, 42, 46, 58, 62, 64, 66, 70, 74, 78, 82, 86, 94, 100, 102, 106, 110, 114, 118, 122, 128, 130, 134, 138, 142, 146, 154, 158, 166, 170, 174, 178, 182, 186, 190, 194, 196, 202, 206, 210, 214, 216, 218, 222

Offset: 1

Gus Wiseman, Nov 30 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

We define the multiset multiplicity kernel MMK(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then min(S) has multiplicity |S| in MMK(m). For example, MMK({1,1,2,2,3,4,5}) = {1,1,3,3,3}, and MMK({1,2,3,4,5,5,5,5}) = {1,1,1,1,5}. As an operation on multisets MMK is represented by A367579, and as an operation on their ranks it is represented by A367580.

			We have MMK({1,1,2,2}) = {1,1} so 36 is in the sequence.
The terms together with their prime indices begin:
    1: {}
    2: {1}
    4: {1,1}
    6: {1,2}
    8: {1,1,1}
   10: {1,3}
   14: {1,4}
   16: {1,1,1,1}
   22: {1,5}
   26: {1,6}
   30: {1,2,3}
   32: {1,1,1,1,1}
   34: {1,7}
   36: {1,1,2,2}
   38: {1,8}
   42: {1,2,4}

Contains all prime powers A000961 and squarefree numbers A005117.
Partitions of this type (uniform containing 1) are counted by A097986.
Positions of all one rows {1,1,...} in A367579.
Positions of powers of 2 in A367580.
A007947 gives squarefree kernel.
A027746 lists prime factors, length A001222, indices A112798.
A027748 lists distinct prime factors, length A001221, indices A304038.
A071625 counts distinct prime exponents.
A124010 gives prime signature, sorted A118914.
A367581 gives multiset multiplicity kernel sum, max A367583, min A055396.
Cf. A001597, A051904, A072774, A130091, A175781, A367584, A367587, A367685.

isA := proc(n) z := padic:-ordp(n, 2); andseq(z=p[2], p in ifactors(n)[2]) end:
select(isA, [seq(1..222)]);  # Peter Luschny, Jun 10 2025

Select[Range[100], #==1||EvenQ[#]&&SameQ@@Last/@FactorInteger[#]&]

Consists of 1 and all even terms of A072774 (powers of squarefree numbers).

A367859 Multiset multiplicity cokernel (MMC) of n. Product of (greatest prime factor with exponent k)^(number of prime factors with exponent k) over all distinct exponents k appearing in the prime factorization of n.

Original entry on oeis.org

1, 2, 3, 2, 5, 9, 7, 2, 3, 25, 11, 6, 13, 49, 25, 2, 17, 6, 19, 10, 49, 121, 23, 6, 5, 169, 3, 14, 29, 125, 31, 2, 121, 289, 49, 9, 37, 361, 169, 10, 41, 343, 43, 22, 15, 529, 47, 6, 7, 10, 289, 26, 53, 6, 121, 14, 361, 841, 59, 50, 61, 961, 21, 2, 169, 1331

Offset: 1

Gus Wiseman, Dec 03 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

We define the multiset multiplicity cokernel MMC(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then max(S) has multiplicity |S| in MMC(m). For example, MMC({1,1,2,2,3,4,5}) = {2,2,5,5,5}, and MMC({1,2,3,4,5,5,5,5}) = {4,4,4,4,5}. As an operation on multisets MMC is represented by A367858, and as an operation on their ranks it is represented by A367859.

			90 has prime factorization 2^1*3^2*5^1, so for k = 1 we have 5^2, and for k = 2 we have 3^1, so a(90) = 75.

Positions of 2's are A000079 without 1.
Positions of 3's are A000244 without 1.
Positions of primes (including 1) are A000961.
Depends only on rootless base A052410, see A007916.
Positions of prime powers are A072774.
Positions of squarefree numbers are A130091.
For kernel instead of cokernel we have A367580, ranks of A367579.
Rows of A367858 have this rank, sum A367860, max A061395, min A367587.
A007947 gives squarefree kernel.
A027746 lists prime factors, length A001222, indices A112798.
A027748 lists distinct prime factors, length A001221, indices A304038.
A071625 counts distinct prime exponents.
A124010 gives multiset of multiplicities (prime signature), sorted A118914.
Cf. A005117, A020639, A052409, A175781, A181819, A353742, A367584, A367585.

mmc[q_]:=With[{mts=Length/@Split[q]}, Sort[Table[Max@@Select[q,Count[q,#]==i&], {i,mts}]]];
Table[Times@@mmc[Join@@ConstantArray@@@FactorInteger[n]], {n,30}]

a(n^k) = a(n) for all positive integers n and k.
If n is squarefree, a(n) = A006530(n)^A001222(n).
A055396(a(n)) = A367587(n).
A056239(a(n)) = A367860(n).
A061395(a(n)) = A061395(n).
A001222(a(n)) = A001221(n).
A001221(a(n)) = A071625(n).
A071625(a(n)) = A323022(n).

A367683 Numbers whose sorted prime signature is the same as the multiset multiplicity kernel of their prime indices.

Original entry on oeis.org

1, 2, 6, 9, 10, 12, 14, 18, 22, 26, 30, 34, 38, 40, 42, 46, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 102, 106, 110, 112, 114, 118, 122, 125, 126, 130, 134, 138, 142, 146, 154, 158, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 218, 222, 225

Offset: 1

Gus Wiseman, Nov 30 2023

nonn

We define the multiset multiplicity kernel (MMK) of a positive integer n to be the product of (least prime factor with exponent k)^(number of prime factors with exponent k) over all distinct exponents k appearing in the prime factorization of n. For example, 90 has prime factorization 2^1 * 3^2 * 5^1, so for k = 1 we have 2^2, and for k = 2 we have 3^1, so MMK(90) = 12. As an operation on multisets MMK is represented by A367579, and as an operation on their ranks it is represented by A367580.

			The terms together with their prime indices begin:
    1: {}
    2: {1}
    6: {1,2}
    9: {2,2}
   10: {1,3}
   12: {1,1,2}
   14: {1,4}
   18: {1,2,2}
   22: {1,5}
   26: {1,6}
   30: {1,2,3}
   34: {1,7}
   38: {1,8}
   40: {1,1,1,3}
   42: {1,2,4}
   46: {1,9}
   58: {1,10}
   62: {1,11}
   66: {1,2,5}
   70: {1,3,4}

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, 20 X 20 color coded list of terms, color function: gray = 1, red = prime, gold = composite prime power, green = squarefree composite, blue-purple = numbers neither squarefree nor prime powers. Bright green = primorial, light green = even squarefree semiprime, light blue = highly composite, middle blue = in A055932, purple = squareful but not a prime power.
Michael De Vlieger, 485 X 485 = 235225-term raster with the same color code as above.

Squarefree terms are A039956.
The LHS is A118914, unsorted A124010.
Prime-power terms are A307539.
The RHS is A367579, ranks A367580, sum A367581, max A367583.
Partitions of this type are counted by A367682.
A007947 gives squarefree kernel.
A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
A181819 gives prime shadow, with an inverse A181821.
A238747 gives prime metasignature, reversed A353742.
A304038 lists distinct prime indices, length A001221, sum A066328.
A367582 counts partitions by sum of multiset multiplicity kernel.
Cf. A000720, A000961, A005117, A051904, A052409, A071625, A072774, A130091, A367584, A367586, A367587.

mmk[q_]:=With[{mts=Length/@Split[q]}, Sort[Table[Min@@Select[q,Count[q,#]==i&], {i,mts}]]];
Select[Range[100], #==1||Sort[Last/@FactorInteger[#]] == mmk[PrimePi/@Join@@ConstantArray@@@FactorInteger[#]]&]

A367858 Irregular triangle read by rows where row n is the multiset multiplicity cokernel (MMC) of the multiset of prime indices of n.

Original entry on oeis.org

1, 2, 1, 3, 2, 2, 4, 1, 2, 3, 3, 5, 1, 2, 6, 4, 4, 3, 3, 1, 7, 1, 2, 8, 1, 3, 4, 4, 5, 5, 9, 1, 2, 3, 6, 6, 2, 1, 4, 10, 3, 3, 3, 11, 1, 5, 5, 7, 7, 4, 4, 2, 2, 12, 8, 8, 6, 6, 1, 3, 13, 4, 4, 4, 14, 1, 5, 2, 3, 9, 9, 15, 1, 2, 4, 1, 3, 7, 7, 1, 6, 16, 1, 2

Offset: 1

Gus Wiseman, Dec 03 2023

Row n = 1 is empty.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
We define the multiset multiplicity cokernel MMC(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then max(S) has multiplicity |S| in MMC(m). For example, MMC({1,1,2,2,3,4,5}) = {2,2,5,5,5}, and MMC({1,2,3,4,5,5,5,5}) = {4,4,4,4,5}.

			The first 45 rows:
     1: {}       16: {1}        31: {11}
     2: {1}      17: {7}        32: {1}
     3: {2}      18: {1,2}      33: {5,5}
     4: {1}      19: {8}        34: {7,7}
     5: {3}      20: {1,3}      35: {4,4}
     6: {2,2}    21: {4,4}      36: {2,2}
     7: {4}      22: {5,5}      37: {12}
     8: {1}      23: {9}        38: {8,8}
     9: {2}      24: {1,2}      39: {6,6}
    10: {3,3}    25: {3}        40: {1,3}
    11: {5}      26: {6,6}      41: {13}
    12: {1,2}    27: {2}        42: {4,4,4}
    13: {6}      28: {1,4}      43: {14}
    14: {4,4}    29: {10}       44: {1,5}
    15: {3,3}    30: {3,3,3}    45: {2,3}

Indices of empty and singleton rows are A000961.
Row lengths are A001221.
Depends only on rootless base A052410, see A007916.
Row maxima are A061395.
Rows have A071625 distinct elements.
Indices of constant rows are A072774.
Indices of strict rows are A130091.
Row minima are A367587.
Rows have Heinz numbers A367859.
Row sums are A367860.
Sorted row indices of first appearances are A367861, for kernel A367585.
A007947 gives squarefree kernel.
A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
A124010 lists prime multiplicities (prime signature), sorted A118914.
A181819 gives prime shadow, with an inverse A181821.
A238747 gives prime metasignature, reversed A353742.
A304038 lists distinct prime indices, length A001221, sum A066328.
Cf. A000720, A027746, A051904, A052409, A061395, A175781, A367582, A367583.

mmc[q_]:=With[{mts=Length/@Split[q]}, Sort[Table[Max@@Select[q,Count[q,#]==i&], {i,mts}]]];
Table[mmc[PrimePi /@ Join@@ConstantArray@@@If[n==1, {},FactorInteger[n]]], {n,100}]

For all positive integers n and k, row n^k is the same as row n.

A367860 Sum of the multiset multiplicity cokernel (in which each multiplicity becomes the greatest element of that multiplicity) of the prime indices of n.

Original entry on oeis.org

0, 1, 2, 1, 3, 4, 4, 1, 2, 6, 5, 3, 6, 8, 6, 1, 7, 3, 8, 4, 8, 10, 9, 3, 3, 12, 2, 5, 10, 9, 11, 1, 10, 14, 8, 4, 12, 16, 12, 4, 13, 12, 14, 6, 5, 18, 15, 3, 4, 4, 14, 7, 16, 3, 10, 5, 16, 20, 17, 7, 18, 22, 6, 1, 12, 15, 19, 8, 18, 12, 20, 3, 21, 24, 5, 9, 10

Offset: 1

Gus Wiseman, Dec 03 2023

nonn

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

We define the multiset multiplicity cokernel MMC(m) of a multiset m by the following property, holding for all distinct multiplicities k >= 1. If S is the set of elements of multiplicity k in m, then max(S) has multiplicity |S| in MMC(m). For example, MMC({1,1,2,2,3,4,5}) = {2,2,5,5,5}, and MMC({1,2,3,4,5,5,5,5}) = {4,4,4,4,5}. As an operation on multisets MMC is represented by A367858, and as an operation on their ranks it is represented by A367859.

			The multiset multiplicity cokernel of {1,2,2,3} is {2,3,3}, so a(90) = 8.

Positions of 1's are A000079 without 1.
Depends only on rootless base A052410, see A007916, A052409.
For kernel instead of cokernel we have A367581, row-sums of A367579.
For minimum instead of sum we have A367587, opposite A367583.
The triangle A367858 has these as row sums, ranks A367859.
A007947 gives squarefree kernel.
A112798 lists prime indices, length A001222, sum A056239, reverse A296150.
A124010 gives prime signature, sorted A118914.
A181819 gives prime shadow, with an inverse A181821.
A238747 gives prime metasignature, reverse A353742.
A304038 lists distinct prime indices, length A001221, sum A066328.
Cf. A000720, A051904, A055396, A061395, A071625, A072774, A130091, A367580, A175781, A367582, A367584.

mmc[q_]:=With[{mts=Length/@Split[q]}, Sort[Table[Max@@Select[q,Count[q,#]==i&], {i,mts}]]];
Table[Total[mmc[PrimePi/@Join@@ConstantArray@@@If[n==1, {},FactorInteger[n]]]],{n,100}]

cp's OEIS Frontend

A367579 Irregular triangle read by rows where row n is the multiset multiplicity kernel (MMK) of the multiset of prime indices of n.

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A367581 Sum of the multiset multiplicity kernel (in which each multiplicity becomes the least element of that multiplicity) of the prime indices of n.

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Mathematica

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A367583 Greatest element in row n of A367579 (multiset multiplicity kernel).

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Mathematica

Formula

A367586 Numbers whose prime indices have a multiset multiplicity kernel (in which each prime exponent becomes the least prime factor with that exponent) that is all ones {1,1,...}. Positions of powers of 2 in A367580.

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Maple

Mathematica

Formula

A367859 Multiset multiplicity cokernel (MMC) of n. Product of (greatest prime factor with exponent k)^(number of prime factors with exponent k) over all distinct exponents k appearing in the prime factorization of n.

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Mathematica

Formula

A367683 Numbers whose sorted prime signature is the same as the multiset multiplicity kernel of their prime indices.

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Mathematica

A367858 Irregular triangle read by rows where row n is the multiset multiplicity cokernel (MMC) of the multiset of prime indices of n.

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Mathematica

Formula

A367860 Sum of the multiset multiplicity cokernel (in which each multiplicity becomes the greatest element of that multiplicity) of the prime indices of n.

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