%I #5 Nov 01 2019 18:41:30
%S 2,4,8,15,16,32,33,35,45,51,55,64,69,75,77,85,93,95,99,119,123,128,
%T 135,141,143,145,153,155,161,165,175,177,187,201,205,207,209,215,217,
%U 219,221,225,245,249,253,255,256,265,275,279,287,291,295,297,309,323
%N Numbers whose distinct prime indices are relatively prime and pairwise indivisible.
%C 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.
%F Intersection of A316476 and A289509.
%e The sequence of terms together with their prime indices begins:
%e 2: {1}
%e 4: {1,1}
%e 8: {1,1,1}
%e 15: {2,3}
%e 16: {1,1,1,1}
%e 32: {1,1,1,1,1}
%e 33: {2,5}
%e 35: {3,4}
%e 45: {2,2,3}
%e 51: {2,7}
%e 55: {3,5}
%e 64: {1,1,1,1,1,1}
%e 69: {2,9}
%e 75: {2,3,3}
%e 77: {4,5}
%e 85: {3,7}
%e 93: {2,11}
%e 95: {3,8}
%e 99: {2,2,5}
%e 119: {4,7}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t Select[Range[100],GCD@@primeMS[#]==1&&stableQ[primeMS[#],Divisible]&]
%Y These are the Heinz numbers of the partitions counted by A328676.
%Y Numbers whose prime indices are relatively prime are A289509.
%Y Partitions whose distinct parts are pairwise indivisible are A305148.
%Y The version for binary indices (instead of prime indices) is A328671.
%Y Cf. A000837, A056239, A112798, A285573, A289508, A303362, A304713, A327393, A328460.
%K nonn
%O 1,1
%A _Gus Wiseman_, Oct 30 2019