A304464 -id:A304464 - cp's OEIS frontend

A319153 Number of integer partitions of n that reduce to 2, meaning their Heinz number maps to 2 under A304464.

0, 2, 1, 3, 5, 7, 12, 17, 24, 33, 44, 57, 76, 100, 129, 168, 214, 282, 355, 462, 586, 755, 937, 1202, 1493, 1900, 2349, 2944, 3621, 4520, 5514, 6813, 8298, 10150, 12240, 14918, 17931, 21654, 25917, 31081, 37029, 44256, 52474, 62405, 73724, 87378, 102887

Offset: 1

Gus Wiseman, Sep 12 2018

nonn

Start with an integer partition y of n. Given a multiset, take the multiset of its multiplicities. Repeat until a multiset of size 1 is obtained. If this multiset is {2}, we say that y reduces to 2. For example, we have (3211) -> (211) -> (21) -> (11) -> (2), so (3211) reduces to 2.

			The a(7) = 12 partitions:
  (43), (52), (61),
  (322), (331), (511),
  (2221), (3211), (4111),
  (22111), (31111),
  (211111).

Cf. A000837, A098859, A181819, A182850, A304464, A304465, A304634, A305563, A317245, A319149.

Table[Length[Select[IntegerPartitions[n],NestWhile[Sort[Length/@Split[#]]&,#,Length[#]>1&]=={2}&]],{n,30}]

A182850 a(n) = number of iterations that n requires to reach a fixed point under the x -> A181819(x) map.

Original entry on oeis.org

0, 0, 1, 2, 1, 3, 1, 2, 2, 3, 1, 4, 1, 3, 3, 2, 1, 4, 1, 4, 3, 3, 1, 4, 2, 3, 2, 4, 1, 3, 1, 2, 3, 3, 3, 3, 1, 3, 3, 4, 1, 3, 1, 4, 4, 3, 1, 4, 2, 4, 3, 4, 1, 4, 3, 4, 3, 3, 1, 5, 1, 3, 4, 2, 3, 3, 1, 4, 3, 3, 1, 4, 1, 3, 4, 4, 3, 3, 1, 4, 2, 3, 1, 5, 3, 3, 3, 4, 1, 5, 3, 4, 3, 3, 3, 4, 1, 4, 4, 3, 1, 3, 1, 4, 3

Offset: 1

Matthew Vandermast, Jan 04 2011

nonn

The fixed points of the x -> A181819(x) map are 1 and 2. Note that the x -> A000005(x) map has the same fixed points, and that A000005(n) = A181819(n) iff n is cubefree (cf. A004709). Under the x -> A181819(x) map, it seems significantly easier to generalize about which kinds of integers take a given number of iterations to reach a fixed point than under the x -> A000005(x) map.

Also the number of steps in the reduction of the multiset of prime factors of n wherein one repeatedly takes the multiset of multiplicities. For example, the a(90) = 5 steps are {2,3,3,5} -> {1,1,2} -> {1,2} -> {1,1} -> {2} -> {1}. - Gus Wiseman, May 13 2018

			A181819(6) = 4; A181819(4) = 3; A181819(3) = 2; A181819(2) = 2. Therefore, a(6) = 3, a(4) = 2, a(3)= 1, and a(2) = 0.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Fixed Point
Eric Weisstein's World of Mathematics, Map

A182857 gives values of n where a(n) increases to a record.

Cf. A000961, A001222, A003434, A005117, A007916, A036459, A112798, A130091, A181819, A182851-A182858, A238748, A304455, A304464, A304465.

a182850 n = length $ takeWhile (`notElem` [1,2]) $ iterate a181819 n
-- Reinhard Zumkeller, Mar 26 2012

Table[If[n<=2,0,Length[FixedPointList[Sort[Length/@Split[#]]&,Sort[Last/@FactorInteger[n]]]]-1],{n,100}] (* Gus Wiseman, May 13 2018 *)

;; With memoization-macro definec.
(definec (A182850 n) (if (<= n 2) 0 (+ 1 (A182850 (A181819 n))))) ;; Antti Karttunen, Feb 05 2016

For n > 2, a(n) = a(A181819(n)) + 1.
a(n) = 0 iff n equals 1 or 2.
a(n) = 1 iff n is an odd prime (A000040(n) for n>1).
a(n) = 2 iff n is a composite perfect prime power (A025475(n) for n>1).
a(n) = 3 iff n is a squarefree composite integer or a power of a squarefree composite integer (cf. A182853).
a(n) = 4 iff n's prime signature a) contains at least two distinct numbers, and b) contains no number that occurs less often than any other number (cf. A182854).

A323023 Irregular triangle read by rows where row n is the omega-sequence of n.

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 1, 2, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 4, 1, 1, 3, 2, 2, 1, 1, 3, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 2, 2, 1, 3, 1, 3, 2, 2, 1, 1, 3, 3, 1, 1, 5, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 4, 2, 1, 1, 2, 2, 1, 2, 2

Offset: 1

Gus Wiseman, Jan 02 2019

We define the omega-sequence of n to have length A323014(n), and the k-th term is Omega(red^{k-1}(n)), where Omega = A001222 and red^{k} is the k-th functional iteration of A181819.

Except for n = 1, all rows end with 1. If n is not prime, the term in row n prior to the last is A304465(n).

			The sequence of omega-sequences begins:
   1:            26: 2 2 1      51: 2 2 1        76: 3 2 2 1
   2: 1          27: 3 1        52: 3 2 2 1      77: 2 2 1
   3: 1          28: 3 2 2 1    53: 1            78: 3 3 1
   4: 2 1        29: 1          54: 4 2 2 1      79: 1
   5: 1          30: 3 3 1      55: 2 2 1        80: 5 2 2 1
   6: 2 2 1      31: 1          56: 4 2 2 1      81: 4 1
   7: 1          32: 5 1        57: 2 2 1        82: 2 2 1
   8: 3 1        33: 2 2 1      58: 2 2 1        83: 1
   9: 2 1        34: 2 2 1      59: 1            84: 4 3 2 2 1
  10: 2 2 1      35: 2 2 1      60: 4 3 2 2 1    85: 2 2 1
  11: 1          36: 4 2 1      61: 1            86: 2 2 1
  12: 3 2 2 1    37: 1          62: 2 2 1        87: 2 2 1
  13: 1          38: 2 2 1      63: 3 2 2 1      88: 4 2 2 1
  14: 2 2 1      39: 2 2 1      64: 6 1          89: 1
  15: 2 2 1      40: 4 2 2 1    65: 2 2 1        90: 4 3 2 2 1
  16: 4 1        41: 1          66: 3 3 1        91: 2 2 1
  17: 1          42: 3 3 1      67: 1            92: 3 2 2 1
  18: 3 2 2 1    43: 1          68: 3 2 2 1      93: 2 2 1
  19: 1          44: 3 2 2 1    69: 2 2 1        94: 2 2 1
  20: 3 2 2 1    45: 3 2 2 1    70: 3 3 1        95: 2 2 1
  21: 2 2 1      46: 2 2 1      71: 1            96: 6 2 2 1
  22: 2 2 1      47: 1          72: 5 2 2 1      97: 1
  23: 1          48: 5 2 2 1    73: 1            98: 3 2 2 1
  24: 4 2 2 1    49: 2 1        74: 2 2 1        99: 3 2 2 1
  25: 2 1        50: 3 2 2 1    75: 3 2 2 1     100: 4 2 1

Row lengths are A323014, or A182850 if we assume A182850(2) = 1.
First column is empty if n = 1 and otherwise A001222(n).
Second column is empty if n is 1 or prime and otherwise A001221(n).
Third column is empty if n is 1, prime, or a power of a prime and otherwise A071625(n).
Cf. A024619, A056239, A067340, A118914, A181819, A181821, A182857, A304464, A304465, A323022.

red[n_]:=Times@@Prime/@Last/@If[n==1,{},FactorInteger[n]];
omg[n_,k_]:=If[k==1,PrimeOmega[n],omg[red[n],k-1]];
dep[n_]:=If[n==1,0,If[PrimeQ[n],1,1+dep[Times@@Prime/@Last/@If[n==1,{},FactorInteger[n]]]]];
Table[omg[n,k],{n,100},{k,dep[n]}]

A318283 Sum of elements of the multiset spanning an initial interval of positive integers with multiplicities equal to the prime indices of n in weakly decreasing order.

Original entry on oeis.org

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

Offset: 1

Gus Wiseman, Aug 23 2018

nonn

			The multiset spanning an initial interval of positive integers with multiplicities equal to the prime indices of 90 in weakly decreasing order is {1,1,1,2,2,3,3,4}, so a(90) = 1+1+1+2+2+3+3+4 = 17.

Row sums of A305936.

Cf. A000041, A000720, A001221, A001222, A056239, A112798, A181821, A182850, A296150, A304464.

nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
Total/@Array[nrmptn,100]

a(n) = A056239(A181821(n)).

A182857 Smallest number that requires exactly n iterations to reach a fixed point under the x -> A181819(x) map.

Original entry on oeis.org

1, 3, 4, 6, 12, 60, 2520, 1286485200, 35933692027611398678865941374040400000

Offset: 0

Matthew Vandermast, Jan 05 2011

nonn

a(9) has 296 digits.
Related to Levine's sequence (A011784): A011784(n) = A001222(a(n)) = A001221(a(n+1)) = A051903(a(n+2)) = A071625(a(n+2)). Also see A182858.
Values of n where A182850(n) increases to a record.
The multiplicity of prime(k) in a(n+1) is the k-th largest prime index of a(n), which is A296150(a(n),k). - Gus Wiseman, May 13 2018

			From _Gus Wiseman_, May 13 2018: (Start)
Like A001462 the following sequence of multisets whose Heinz numbers belong to this sequence is a run-length describing sequence, as the number of k's in row n + 1 is equal to the k-th term of row n.
{2}
{1,1}
{1,2}
{1,1,2}
{1,1,2,3}
{1,1,1,2,2,3,4}
{1,1,1,1,2,2,2,3,3,4,4,5,6,7}
{1,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,7,7,7,8,8,9,9,10,10,11,12,13,14}
(End)

Gus Wiseman, Table of n, a(n) for n = 0..9

Cf. A001462, A007755, A007916, A009287, A012257, A112798, A181819, A182850-A182858, A296150, A304455, A304464, A304465.

Prepend[Function[m,Times@@Prime/@m]/@NestList[Join@@Table[Table[i,{Reverse[#][[i]]}],{i,Length[#]}]&,{2},8],1] (* Gus Wiseman, May 13 2018 *)

For n > 0, a(n) = A181819(a(n+1)). For n > 1, a(n) = A181821(a(n-1)).

A305936 Irregular triangle whose n-th row is the multiset spanning an initial interval of positive integers with multiplicities equal to the n-th row of A296150 (the prime indices of n in weakly decreasing order).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 3, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 2, 2, 1

Offset: 1

Gus Wiseman, Aug 23 2018

			Row 90 is {1,1,1,2,2,3,3,4} because 90 = prime(3)*prime(2)*prime(2)*prime(1).
Triangle begins:
   1:
   2:  1
   3:  1  1
   4:  1  2
   5:  1  1  1
   6:  1  1  2
   7:  1  1  1  1
   8:  1  2  3
   9:  1  1  2  2
  10:  1  1  1  2
  11:  1  1  1  1  1
  12:  1  1  2  3
  13:  1  1  1  1  1  1

Row lengths are A056239. Number of distinct elements in row n is A001222(n). Number of distinct multiplicities in row n is A001221(n).
Cf. A000041, A000720, A112798, A181821, A182850, A255906, A296150, A304464.
Cf. A318283, A318284, A318285, A318286, A318287, A318360, A318361, A318362, A318371.

nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
Array[nrmptn,30]

A304465 If n is prime, set a(n) = 1. Otherwise, start with the multiset of prime factors of n, and given a multiset take the multiset of its multiplicities. Repeating this until a multiset of size 1 is reached, set a(n) to the unique element of this multiset.

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 3, 1, 5, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 6, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 4, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 2, 3

Offset: 1

Gus Wiseman, May 13 2018

nonn

a(1) = 0 by convention.

a(n) depends only on prime signature of n (cf. A025487). - Antti Karttunen, Nov 08 2018

			Starting with the multiset of prime factors of 2520 we have {2,2,2,3,3,5,7} -> {1,1,2,3} -> {1,1,2} -> {1,2} -> {1,1} -> {2}, so a(2520) = 2.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
Index entries for sequences computed from exponents in factorization of n

Cf. A000005, A001222, A001597, A005117, A007916, A055932, A056239, A112798, A181819, A182850, A182857, A275870, A296150, A303945, A304464.

Table[Switch[n,1,0,?PrimeQ,1,,NestWhile[Sort[Length/@Split[#]]&,Sort[Last/@FactorInteger[n]],Length[#]>1&]//First],{n,100}]

A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A304465(n) = if(1==n,0,my(t=isprimepower(n)); if(t,t, t=omega(n); if(bigomega(n)==t),t,A304465(A181819(n)))); \\ Antti Karttunen, Nov 08 2018

a(p^n) = n where p is any prime number.
a(product of n distinct primes) = n.
a(1) = 0; and for n > 1, if n = prime^k, a(n) = k, otherwise, if n is squarefree [i.e., A001221(n) = A001222(n)], a(n) = A001221(n), otherwise a(n) = a(A181819(n)). - Antti Karttunen, Nov 08 2018

More terms from Antti Karttunen, Nov 08 2018

A323022 Fourth omega of n. Number of distinct multiplicities in the prime signature of n.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Gus Wiseman, Jan 02 2019

nonn

The indices of terms greater than 1 are {60, 84, 90, 120, 126, 132, 140, 150, ...}.
First term greater than 2 is a(1801800) = 3. In general, the first appearance of k is a(A182856(k)) = k.
The prime signature of n (row n of A118914) is the multiset of prime multiplicities in n.
We define the k-th omega of n to be Omega(red^{k-1}(n)) where Omega = A001222 and red^{k} is the k-th functional iteration of A181819. The first three omegas are A001222, A001221, A071625, and this sequence is the fourth. The zeroth omega is not uniquely determined from prime signature, but one possible choice is A056239 (sum of prime indices).

			The prime signature of 1286485200 is {1, 1, 1, 2, 2, 3, 4}, in which 1 appears three times, two appears twice, and 3 and 4 both appear once, so there are 3 distinct multiplicities {1, 2, 3} and hence a(1286485200) = 3.

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A001221, A001222, A006939, A025487, A056239, A059404, A062770, A071625, A118914, A181819, A182856, A182857, A304464, A304465, A323014, A323023.

red[n_]:=Times@@Prime/@Last/@If[n==1,{},FactorInteger[n]];
Table[PrimeNu[red[red[n]]],{n,200}]

a(n) = my(e=factor(n)[, 2], s = Set(e), m=Map(), v=vector(#s)); for(i=1, #s, mapput(m,s[i],i)); for(i=1, #e, v[mapget(m,e[i])]++); #Set(v) \\ David A. Corneth, Jan 02 2019

A071625(n) = #Set(factor(n)[, 2]); \\ From A071625
A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A323022(n) = A071625(A181819(n)); \\ Antti Karttunen, Jan 03 2019

a(n) = A071625(A181819(n))
     = A001221(A181819(A181819(n)))
     = A001222(A181819(A181819(A181819(n))))
     = A056239(A181819(A181819(A181819(A181819(n))))).

More terms from Antti Karttunen, Jan 03 2019

A304455 Number of steps in the reduction to a multiset of size 1 of the multiset of prime factors of n, obtained by repeatedly taking the multiset of multiplicities.

Original entry on oeis.org

0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 3, 0, 2, 2, 1, 0, 3, 0, 3, 2, 2, 0, 3, 1, 2, 1, 3, 0, 2, 0, 1, 2, 2, 2, 2, 0, 2, 2, 3, 0, 2, 0, 3, 3, 2, 0, 3, 1, 3, 2, 3, 0, 3, 2, 3, 2, 2, 0, 4, 0, 2, 3, 1, 2, 2, 0, 3, 2, 2, 0, 3, 0, 2, 3, 3, 2, 2, 0, 3, 1, 2, 0, 4, 2, 2, 2, 3, 0, 4, 2, 3, 2, 2, 2, 3, 0, 3, 3, 2, 0, 2, 0, 3, 2

Offset: 1

Gus Wiseman, May 12 2018

nonn

			The a(2520) = 5 steps are {2,2,2,3,3,5,7} -> {1,1,2,3} -> {1,1,2} -> {1,2} -> {1,1} -> {2}.

Antti Karttunen, Table of n, a(n) for n = 1..20000
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
Index entries for sequences computed from exponents in factorization of n

Cf. A000961, A001222, A001597, A005117, A007916, A055932, A056239, A112798, A130091, A181819, A182850, A182853, A182857, A303945, A304464, A304465, A320118.

Table[Length[Select[FixedPointList[Sort[Length/@Split[#]]&,If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[p,{k}]]]]],Length[#]>1&]],{n,100}]

A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A304455(n) = if(n<=2,0, n=A181819(n); if(2==n,0,1+A304455(n))); \\ Antti Karttunen, Dec 06 2018

For n > 2, a(n) = A182850(n) - 1.
a(prime(n)) = 0.
a(A246547(n)) = 1.

More terms from Antti Karttunen, Dec 06 2018

A319151 Heinz numbers of superperiodic integer partitions.

Original entry on oeis.org

2, 3, 5, 7, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233

Offset: 1

Gus Wiseman, Sep 12 2018

nonn

First differs from A061345 at a(1) = 2 and next at a(98) = 441.
A number n is in the sequence iff n = 2 or the prime indices of n have a common divisor > 1 and the Heinz number of the multiset of prime multiplicities of n, namely A181819(n), is already in the sequence.
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

			The sequence of partitions whose Heinz numbers belong to the sequence begins: (1), (2), (3), (4), (2,2), (5), (6), (7), (8), (9), (3,3), (2,2,2), (10), (11), (12), (13), (14), (15), (4,4), (16), (17), (18), (19), (20), (21), (22), (2,2,2,2).

Vincenzo Librandi, Table of n, a(n) for n = 1..2326

Cf. A001597, A056239, A072774, A098859, A181819, A182850, A289509, A296150, A298748, A304464, A305732, A317246, A317257, A319149, A319152, A319157.

supperQ[n_]:=Or[n==2,And[GCD@@PrimePi/@FactorInteger[n][[All,1]]>1,supperQ[Times@@Prime/@FactorInteger[n][[All,2]]]]];
Select[Range[500],supperQ]

cp's OEIS Frontend

A319153 Number of integer partitions of n that reduce to 2, meaning their Heinz number maps to 2 under A304464.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A182850 a(n) = number of iterations that n requires to reach a fixed point under the x -> A181819(x) map.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Mathematica

Scheme

Formula

A323023 Irregular triangle read by rows where row n is the omega-sequence of n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A318283 Sum of elements of the multiset spanning an initial interval of positive integers with multiplicities equal to the prime indices of n in weakly decreasing order.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

A182857 Smallest number that requires exactly n iterations to reach a fixed point under the x -> A181819(x) map.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A305936 Irregular triangle whose n-th row is the multiset spanning an initial interval of positive integers with multiplicities equal to the n-th row of A296150 (the prime indices of n in weakly decreasing order).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A304465 If n is prime, set a(n) = 1. Otherwise, start with the multiset of prime factors of n, and given a multiset take the multiset of its multiplicities. Repeating this until a multiset of size 1 is reached, set a(n) to the unique element of this multiset.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A323022 Fourth omega of n. Number of distinct multiplicities in the prime signature of n.

Views

Author

Keywords

Comments

Examples

Links