A304713 -id:A304713 - cp's OEIS frontend

A316474 Number of locally stable rooted identity trees with n nodes, meaning no branch is a subset of any other branch of the same root.

1, 1, 1, 1, 1, 2, 3, 5, 8, 14, 23, 42, 73, 133, 241, 442, 812, 1508, 2802, 5247, 9842, 18554, 35045, 66453, 126249

Offset: 1

Gus Wiseman, Jul 04 2018

			The a(9) = 8 locally stable rooted identity trees:
((((((((o))))))))
(((((o)((o))))))
((((o)(((o))))))
(((o)((((o))))))
((((o))(((o)))))
((o)(((((o))))))
((o)((o)((o))))
(((o))((((o)))))

Gus Wiseman, The a(10) = 14 locally stable rooted identity trees with 10 nodes.

Cf. A000081, A004111, A276625, A277098, A285572, A285573, A303362, A304713, A316467, A316471, A316471, A316475.

strut[n_]:=strut[n]=If[n===1,{{}},Select[Join@@Function[c,Union[Sort/@Tuples[strut/@c]]]/@IntegerPartitions[n-1],UnsameQ@@#&&Select[Tuples[#,2],UnsameQ@@#&&Complement@@#=={}&]=={}&]];
Table[Length[strut[n]],{n,20}]

A316494 Matula-Goebel numbers of locally disjoint rooted identity trees, meaning no branch overlaps any other branch of the same root.

Original entry on oeis.org

1, 2, 3, 5, 6, 10, 11, 13, 15, 22, 26, 29, 30, 31, 33, 41, 47, 55, 58, 62, 66, 79, 82, 93, 94, 101, 109, 110, 113, 123, 127, 137, 141, 143, 145, 155, 158, 165, 179, 186, 202, 205, 211, 218, 226, 246, 254, 257, 271, 274, 282, 286, 290, 293, 310, 317, 327, 330

Offset: 1

Gus Wiseman, Jul 04 2018

nonn

A prime index of n is a number m such that prime(m) divides n. A number is in the sequence iff either it is equal to 1, it is a prime number whose prime index already belongs to the sequence, or its prime indices are pairwise coprime, distinct, and already belong to the sequence.

			The sequence of all locally disjoint rooted identity trees preceded by their Matula-Goebel numbers begins:
   1: o
   2: (o)
   3: ((o))
   5: (((o)))
   6: (o(o))
  10: (o((o)))
  11: ((((o))))
  13: ((o(o)))
  15: ((o)((o)))
  22: (o(((o))))
  26: (o(o(o)))
  29: ((o((o))))
  30: (o(o)((o)))
  31: (((((o)))))

Cf. A000081, A004111, A007097, A276625, A277098, A302696, A303362, A304713, A316467, A316471, A316474, A316495.

primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[1000],Or[#==1,And[SquareFreeQ[#],Or[PrimeQ[#],CoprimeQ@@primeMS[#]],And@@#0/@primeMS[#]]]&]

A322437 Number of unordered pairs of factorizations of n into factors > 1 where no factor of one divides any factor of the other.

Original entry on oeis.org

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

Offset: 1

Gus Wiseman, Dec 08 2018

nonn

First differs from A322438 at a(144) = 3, A322438(144) = 4.
From Antti Karttunen, Dec 11 2020: (Start)
Zeros occur on numbers that are either of the form p^k, or q * p^k, or p*q*r, for some primes p, q, r, and exponent k >= 0. [Note also that in all these cases, when x > 1, A307408(x) = 2+A307409(x) = 2 + (A001222(x) - 1)*A001221(x) = A000005(x)].
Proof:
  It is easy to see that for such numbers it is not possible to obtain two such distinct factorizations, that no factor of the other would not divide some factor of the other.
  Conversely, the complement set of above is formed of such composites n that have at least one unitary divisor that is either of the form
  (1) p^x * q^y, with x, y >= 2,
  or
  (2) p^x * q^y * r^z, with x >= 2, and y, z >= 1,
  or
  (3) p^x * q^y * r^z * s^w, with x, y, z, w >= 1,
  where p, q, r, s are distinct primes. Let's indicate with C the remaining portion of k coprime to p, q, r and s (which could be also 1). Then in case (1) we can construct two factorizations, the first having factors (p*q*C) and (p^(x-1) * q^(y-1)), and the second having factors (p^x * C) and (q^y) that are guaranteed to satisfy the condition that no factor in the other factorization divides any of the factors of the other factorization. For case (2) pairs like {(p * q^y * C), (p^(x-1) * r^z)} and {(p^x * C), (q^y * r^z)}, and for case (3) pairs like {(p^x * q^y * C), (r^z * s^w)} and {(p^x * r^z * C), (q^y * s^w)} offer similar examples, therefore a(n) > 0 for all such cases.
(End)

			The a(120) = 2 pairs of such factorizations:
   (6*20)|(8*15)
   (8*15)|(10*12)
The a(144) = 3 pairs of factorizations:
   (6*24)|(9,16)
   (8*18)|(12*12)
   (9*16)|(12*12)
The a(210) = 3 pairs of factorizations:
   (6*35)|(10*21)
   (6*35)|(14*15)
  (10*21)|(14*15)
[Note that 210 is the first squarefree number obtaining nonzero value]
The a(240) = 4 pairs of factorizations:
   (6*40)|(15*16)
   (8*30)|(12*20)
  (10*24)|(15*16)
  (12*20)|(15*16)
The a(1728) = 14 pairs of factorizations:
    (6*6*48)|(27*64)
   (6*12*24)|(27*64)
     (6*288)|(27*64)
    (8*8*27)|(12*12*12)
  (12*12*12)|(27*64)
  (12*12*12)|(32*54)
    (12*144)|(27*64)
    (12*144)|(32*54)
    (16*108)|(24*72)
     (18*96)|(27*64)
     (24*72)|(27*64)
     (24*72)|(32*54)
     (27*64)|(36*48)
     (32*54)|(36*48)

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from exponents in factorization of n

Cf. A000688, A001055, A285572, A285573, A294068, A303362, A304713, A305149, A305150, A305193, A316476, A317144, A322435, A322436, A322441, A322442, A339626.

Cf. also comments A307408 and A307409.

facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
Table[Length[Select[Subsets[facs[n],{2}],And[!Or@@Divisible@@@Tuples[#],!Or@@Divisible@@@Reverse/@Tuples[#]]&]],{n,100}]

factorizations(n, m=n, f=List([]), z=List([])) = if(1==n, listput(z,Vec(f)); z, my(newf); fordiv(n, d, if((d>1)&&(d<=m), newf = List(f); listput(newf,d); z = factorizations(n/d, d, newf, z))); (z));
is_ndf_pair(fac1,fac2) = { for(i=1,#fac1,for(j=1,#fac2,if(!(fac1[i]%fac2[j])||!(fac2[j]%fac1[i]),return(0)))); (1); };
number_of_ndfpairs(z) = sum(i=1,#z,sum(j=i+1,#z,is_ndf_pair(z[i],z[j])));
A322437(n) = number_of_ndfpairs(Vec(factorizations(n))); \\ Antti Karttunen, Dec 10 2020

For n > 0, a(A002110(n)) = A322441(n)/2 = A339626(n). - Antti Karttunen, Dec 10 2020

Data section extended up to a(120) and more examples added by Antti Karttunen, Dec 10 2020

A328603 Numbers whose prime indices have no consecutive divisible parts, meaning no prime index is a divisor of the next-smallest prime index, counted with multiplicity.

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 51, 53, 55, 59, 61, 67, 69, 71, 73, 77, 79, 83, 85, 89, 91, 93, 95, 97, 101, 103, 105, 107, 109, 113, 119, 123, 127, 131, 137, 139, 141, 143, 145, 149, 151, 155, 157, 161, 163, 165, 167

Offset: 1

Gus Wiseman, Oct 26 2019

nonn

First differs from A304713 in having 105, with prime indices {2, 3, 4}.

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.

			The sequence of terms together with their prime indices begins:
    1: {}
    2: {1}
    3: {2}
    5: {3}
    7: {4}
   11: {5}
   13: {6}
   15: {2,3}
   17: {7}
   19: {8}
   23: {9}
   29: {10}
   31: {11}
   33: {2,5}
   35: {3,4}
   37: {12}
   41: {13}
   43: {14}
   47: {15}
   51: {2,7}

A subset of A005117.
These are the Heinz numbers of the partitions counted by A328171.
The non-strict version is A328674 (Heinz numbers for A328675).
The version for relatively prime instead of indivisible is A328335.
Compositions without consecutive divisibilities are A328460.
Numbers whose binary indices lack consecutive divisibilities are A328593.
The version with all pairs indivisible is A304713.
Cf. A056239, A112798, A316476, A318726, A318729, A326704, A328336, A328598, A328599.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[100],!MatchQ[primeMS[#],{_,x_,y_,_}/;Divisible[y,x]]&]

Intersection of A005117 and A328674.

A328677 Numbers whose distinct prime indices are relatively prime and pairwise indivisible.

Original entry on oeis.org

2, 4, 8, 15, 16, 32, 33, 35, 45, 51, 55, 64, 69, 75, 77, 85, 93, 95, 99, 119, 123, 128, 135, 141, 143, 145, 153, 155, 161, 165, 175, 177, 187, 201, 205, 207, 209, 215, 217, 219, 221, 225, 245, 249, 253, 255, 256, 265, 275, 279, 287, 291, 295, 297, 309, 323

Offset: 1

Gus Wiseman, Oct 30 2019

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. Stable numbers are listed in A316476.

			The sequence of terms together with their prime indices begins:
    2: {1}
    4: {1,1}
    8: {1,1,1}
   15: {2,3}
   16: {1,1,1,1}
   32: {1,1,1,1,1}
   33: {2,5}
   35: {3,4}
   45: {2,2,3}
   51: {2,7}
   55: {3,5}
   64: {1,1,1,1,1,1}
   69: {2,9}
   75: {2,3,3}
   77: {4,5}
   85: {3,7}
   93: {2,11}
   95: {3,8}
   99: {2,2,5}
  119: {4,7}

These are the Heinz numbers of the partitions counted by A328676.
Numbers whose prime indices are relatively prime are A289509.
Partitions whose distinct parts are pairwise indivisible are A305148.
The version for binary indices (instead of prime indices) is A328671.
Cf. A000837, A056239, A112798, A285573, A289508, A303362, A304713, A327393, A328460.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
Select[Range[100],GCD@@primeMS[#]==1&&stableQ[primeMS[#],Divisible]&]

Intersection of A316476 and A289509.

A317102 Powerful numbers whose distinct prime multiplicities are pairwise indivisible.

Original entry on oeis.org

1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 169, 196, 200, 216, 225, 243, 256, 288, 289, 343, 361, 392, 432, 441, 484, 500, 512, 529, 625, 648, 675, 676, 729, 800, 841, 864, 900, 961, 968, 972, 1000, 1024, 1089, 1125, 1152, 1156, 1225

Offset: 1

Gus Wiseman, Aug 01 2018

nonn

A number is powerful if its prime multiplicities are all greater than 1.

			144 = 2^4 * 3^2 is not in the sequence because 4 and 2 are not pairwise indivisible.

Robert Israel, Table of n, a(n) for n = 1..3000

Cf. A001694, A056239, A112798, A118914, A124010, A285572, A285573, A303362, A304713, A316475, A317101, A317616.

filter:= proc(n) local L,i,j,q;
  L:= convert(map(t -> t[2],ifactors(n)[2]),set);
  if min(L) = 1 then return false fi;
  for j from 2 to nops(L) do
    for i from 1 to j-1 do
      q:= L[i]/L[j];
      if q::integer or (1/q)::integer then return false fi;
  od od;
  true
end proc:
select(filter, [$4..10000]); # Robert Israel, Jun 23 2019

Select[Range[1000],And[Max@@Last/@FactorInteger[#]>=2,Select[Tuples[Last/@FactorInteger[#],2],And[UnsameQ@@#,Divisible@@#]&]=={}]&]

Definition corrected and a(1)=1 inserted by Robert Israel, Jun 23 2019

A318727 Number of integer compositions of n where adjacent parts are indivisible (either way) and the last and first part are also indivisible (either way).

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 5, 3, 5, 13, 9, 23, 15, 37, 45, 63, 115, 131, 207, 265, 415, 603, 823, 1251, 1673, 2521, 3519, 5147, 7409, 10449, 15225, 21497, 31285, 44719, 64171, 92315, 131619, 190085, 271871, 391189, 560979, 804265, 1155977, 1656429, 2381307, 3414847

Offset: 1

Gus Wiseman, Sep 02 2018

nonn

			The a(10) = 13 compositions:
  (10)
  (7,3) (3,7) (6,4) (4,6)
  (5,3,2) (5,2,3) (3,5,2) (3,2,5) (2,5,3) (2,3,5)
  (3,2,3,2) (2,3,2,3)

Andrew Howroyd, Table of n, a(n) for n = 1..200

Cf. A000740, A008965, A167606, A285573, A296302, A303362, A304713, A316476, A318726.

Table[Select[Join@@Permutations/@IntegerPartitions[n],!MatchQ[#,({_,x_,y_,_}/;Divisible[x,y]||Divisible[y,x])|({y_,_,x_}/;Divisible[x,y]||Divisible[y,x])]&]//Length,{n,20}]

b(n,k,pred)={my(M=matrix(n,n)); for(n=1, n, M[n,n]=pred(k,n); for(j=1, n-1, M[n,j]=sum(i=1, n-j, if(pred(i,j), M[n-j,i], 0)))); sum(i=1, n, if(pred(i,k), M[n,i], 0))}
a(n)={1 + sum(k=1, n-1, b(n-k, k, (i,j)->i%j<>0&&j%i<>0))} \\ Andrew Howroyd, Sep 08 2018

a(21)-a(28) from Robert Price, Sep 07 2018

Terms a(29) and beyond from Andrew Howroyd, Sep 08 2018

A328671 Numbers whose binary indices are relatively prime and pairwise indivisible.

Original entry on oeis.org

1, 6, 12, 18, 20, 22, 24, 28, 48, 56, 66, 68, 70, 72, 76, 80, 82, 84, 86, 88, 92, 96, 104, 112, 120, 132, 144, 148, 176, 192, 196, 208, 212, 224, 240, 258, 264, 272, 274, 280, 296, 304, 312, 320, 322, 328, 336, 338, 344, 352, 360, 368, 376, 384, 400, 416, 432

Offset: 1

Gus Wiseman, Oct 29 2019

nonn

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

			The sequence of terms together with their binary expansions and binary indices begins:
    1:         1 ~ {1}
    6:       110 ~ {2,3}
   12:      1100 ~ {3,4}
   18:     10010 ~ {2,5}
   20:     10100 ~ {3,5}
   22:     10110 ~ {2,3,5}
   24:     11000 ~ {4,5}
   28:     11100 ~ {3,4,5}
   48:    110000 ~ {5,6}
   56:    111000 ~ {4,5,6}
   66:   1000010 ~ {2,7}
   68:   1000100 ~ {3,7}
   70:   1000110 ~ {2,3,7}
   72:   1001000 ~ {4,7}
   76:   1001100 ~ {3,4,7}
   80:   1010000 ~ {5,7}
   82:   1010010 ~ {2,5,7}
   84:   1010100 ~ {3,5,7}
   86:   1010110 ~ {2,3,5,7}
   88:   1011000 ~ {4,5,7}

The version for prime indices (instead of binary indices) is A328677.
Numbers whose binary indices are relatively prime are A291166.
Numbers whose distinct prime indices are pairwise indivisible are A316476.
BII-numbers of antichains are A326704.
Relatively prime partitions whose distinct parts are pairwise indivisible are A328676, with strict case A328678.
Cf. A000120, A121016, A285573, A303362, A304713, A305148, A316468, A316475.

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
Select[Range[100],GCD@@bpe[#]==1&&stableQ[bpe[#],Divisible]&]

Intersection of A291166 with A326704.

A371294 Numbers whose binary indices are connected and pairwise indivisible, where two numbers are connected iff they have a common factor. A hybrid ranking sequence for connected antichains of multisets.

Original entry on oeis.org

1, 2, 4, 8, 16, 32, 40, 64, 128, 160, 256, 288, 296, 416, 512, 520, 544, 552, 640, 672, 800, 808, 928, 1024, 2048, 2176, 2304, 2432, 2560, 2688, 2816, 2944, 4096, 8192, 8200, 8224, 8232, 8320, 8352, 8480, 8488, 8608, 8704, 8712, 8736, 8744, 8832, 8864, 8992

Offset: 1

Gus Wiseman, Mar 28 2024

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.

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.

			The terms together with their prime indices of binary indices begin:
    1: {{}}
    2: {{1}}
    4: {{2}}
    8: {{1,1}}
   16: {{3}}
   32: {{1,2}}
   40: {{1,1},{1,2}}
   64: {{4}}
  128: {{1,1,1}}
  160: {{1,2},{1,1,1}}
  256: {{2,2}}
  288: {{1,2},{2,2}}
  296: {{1,1},{1,2},{2,2}}
  416: {{1,2},{1,1,1},{2,2}}
  512: {{1,3}}
  520: {{1,1},{1,3}}
  544: {{1,2},{1,3}}
  552: {{1,1},{1,2},{1,3}}
  640: {{1,1,1},{1,3}}
  672: {{1,2},{1,1,1},{1,3}}
  800: {{1,2},{2,2},{1,3}}
  808: {{1,1},{1,2},{2,2},{1,3}}
  928: {{1,2},{1,1,1},{2,2},{1,3}}

Connected case of A087086, relatively prime A328671.
For binary indices of binary indices we have A326750, non-primitive A326749.
For prime indices of prime indices we have A329559, non-primitive A305078.
Primitive case of A371291 = positions of ones in A371452.
For binary indices of prime indices we have A371445, non-primitive A325118.
A001187 counts connected graphs.
A007718 counts non-isomorphic connected multiset partitions.
A048143 counts connected antichains of sets.
A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
A326964 counts connected set-systems, covering A323818.
Cf. A001222, A051026, A285572, A303362, A304713, A305079, A316476, A319496, A319719, A326704, A371446.

stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
prix[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[1000],stableQ[bpe[#],Divisible]&&connectedQ[prix/@bpe[#]]&]

Intersection of A087086 and A371291.

A319837 Numbers whose distinct prime indices are pairwise indivisible and whose own prime indices span an initial interval of positive integers.

Original entry on oeis.org

1, 2, 3, 4, 7, 8, 9, 13, 15, 16, 19, 27, 32, 35, 37, 45, 49, 53, 61, 64, 69, 75, 81, 89, 91, 95, 113, 128, 131, 135, 141, 143, 145, 151, 161, 165, 169, 175, 207, 223, 225, 243, 245, 247, 251, 256, 265, 281, 299, 309, 311, 329, 343, 355, 359, 361, 375, 377, 385

Offset: 1

Gus Wiseman, Dec 16 2018

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. The multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}. This sequence lists all MM-numbers of not necessarily strict antichains of multisets spanning an initial interval of positive integers.

			The sequence of multisystems whose MM-numbers belong to the sequence begins:
   1: {}
   2: {{}}
   3: {{1}}
   4: {{},{}}
   7: {{1,1}}
   8: {{},{},{}}
   9: {{1},{1}}
  13: {{1,2}}
  15: {{1},{2}}
  16: {{},{},{},{}}
  19: {{1,1,1}}
  27: {{1},{1},{1}}
  32: {{},{},{},{},{}}
  35: {{2},{1,1}}
  37: {{1,1,2}}
  45: {{1},{1},{2}}
  49: {{1,1},{1,1}}
  53: {{1,1,1,1}}
  61: {{1,2,2}}
  64: {{},{},{},{},{},{}}
  69: {{1},{2,2}}
  75: {{1},{2},{2}}
  81: {{1},{1},{1},{1}}
  89: {{1,1,1,2}}
  91: {{1,1},{1,2}}
  95: {{2},{1,1,1}}

Cf. A003963, A006126, A055932, A056239, A112798, A285572, A290103, A293993, A302242, A304713, A316476, A318401, A319721, A320275, A320456.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
normQ[sys_]:=Or[Length[sys]==0,Union@@sys==Range[Max@@Max@@sys]];
stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
Select[Range[200],And[normQ[primeMS/@primeMS[#]],stableQ[primeMS[#],Divisible]]&]

cp's OEIS Frontend

A316474 Number of locally stable rooted identity trees with n nodes, meaning no branch is a subset of any other branch of the same root.

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A316494 Matula-Goebel numbers of locally disjoint rooted identity trees, meaning no branch overlaps any other branch of the same root.

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A322437 Number of unordered pairs of factorizations of n into factors > 1 where no factor of one divides any factor of the other.

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Mathematica

PARI

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A328603 Numbers whose prime indices have no consecutive divisible parts, meaning no prime index is a divisor of the next-smallest prime index, counted with multiplicity.

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Mathematica

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A328677 Numbers whose distinct prime indices are relatively prime and pairwise indivisible.

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Mathematica

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A317102 Powerful numbers whose distinct prime multiplicities are pairwise indivisible.

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Maple

Mathematica

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A318727 Number of integer compositions of n where adjacent parts are indivisible (either way) and the last and first part are also indivisible (either way).

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Mathematica

PARI

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A328671 Numbers whose binary indices are relatively prime and pairwise indivisible.

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