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

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

1,1

Comments

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.

Links

Table of n, a(n) for n=1..56.

Formula

Intersection of A316476 and A289509.

Example

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}

Mathematica

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]&]

Crossrefs

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.

Sequence in context: A354192 A076351 A140117 * A039743 A070008 A033623

Adjacent sequences: A328674 A328675 A328676 * A328678 A328679 A328680

Keyword

nonn

Author

Gus Wiseman, Oct 30 2019

Status

approved