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

Author

Gus Wiseman, Oct 30 2019

Keywords

• nonn

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.

Examples

			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}
		

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.

Programs

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]&]

Formula

Intersection of A316476 and A289509.