cp's OEIS Frontend

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

%I A328677 #5 Nov 01 2019 18:41:30
%S A328677 2,4,8,15,16,32,33,35,45,51,55,64,69,75,77,85,93,95,99,119,123,128,
%T A328677 135,141,143,145,153,155,161,165,175,177,187,201,205,207,209,215,217,
%U A328677 219,221,225,245,249,253,255,256,265,275,279,287,291,295,297,309,323
%N A328677 Numbers whose distinct prime indices are relatively prime and pairwise indivisible.
%C A328677 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 A328677 Intersection of A316476 and A289509.
%e A328677 The sequence of terms together with their prime indices begins:
%e A328677     2: {1}
%e A328677     4: {1,1}
%e A328677     8: {1,1,1}
%e A328677    15: {2,3}
%e A328677    16: {1,1,1,1}
%e A328677    32: {1,1,1,1,1}
%e A328677    33: {2,5}
%e A328677    35: {3,4}
%e A328677    45: {2,2,3}
%e A328677    51: {2,7}
%e A328677    55: {3,5}
%e A328677    64: {1,1,1,1,1,1}
%e A328677    69: {2,9}
%e A328677    75: {2,3,3}
%e A328677    77: {4,5}
%e A328677    85: {3,7}
%e A328677    93: {2,11}
%e A328677    95: {3,8}
%e A328677    99: {2,2,5}
%e A328677   119: {4,7}
%t A328677 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A328677 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A328677 Select[Range[100],GCD@@primeMS[#]==1&&stableQ[primeMS[#],Divisible]&]
%Y A328677 These are the Heinz numbers of the partitions counted by A328676.
%Y A328677 Numbers whose prime indices are relatively prime are A289509.
%Y A328677 Partitions whose distinct parts are pairwise indivisible are A305148.
%Y A328677 The version for binary indices (instead of prime indices) is A328671.
%Y A328677 Cf. A000837, A056239, A112798, A285573, A289508, A303362, A304713, A327393, A328460.
%K A328677 nonn
%O A328677 1,1
%A A328677 _Gus Wiseman_, Oct 30 2019