cp's OEIS Frontend

A329366 Numbers whose distinct prime indices are pairwise indivisible (stable) and pairwise non-relatively prime (intersecting).

%I A329366 #5 Nov 12 2019 19:24:15
%S A329366 1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43,47,49,53,
%T A329366 59,61,64,67,71,73,79,81,83,89,91,97,101,103,107,109,113,121,125,127,
%U A329366 128,131,137,139,149,151,157,163,167,169,173,179,181,191,193,197
%N A329366 Numbers whose distinct prime indices are pairwise indivisible (stable) and pairwise non-relatively prime (intersecting).
%C A329366 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.
%C A329366 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). A partition with no two distinct parts divisible is said to be stable, and a partition with no two distinct parts relatively prime is said to be intersecting, so these are Heinz numbers of stable intersecting partitions.
%e A329366 The sequence of terms together with their prime indices begins:
%e A329366     1: {}
%e A329366     2: {1}
%e A329366     3: {2}
%e A329366     4: {1,1}
%e A329366     5: {3}
%e A329366     7: {4}
%e A329366     8: {1,1,1}
%e A329366     9: {2,2}
%e A329366    11: {5}
%e A329366    13: {6}
%e A329366    16: {1,1,1,1}
%e A329366    17: {7}
%e A329366    19: {8}
%e A329366    23: {9}
%e A329366    25: {3,3}
%e A329366    27: {2,2,2}
%e A329366    29: {10}
%e A329366    31: {11}
%e A329366    32: {1,1,1,1,1}
%e A329366    37: {12}
%t A329366 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A329366 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A329366 Select[Range[100],stableQ[Union[primeMS[#]],GCD[#1,#2]==1&]&&stableQ[Union[primeMS[#]],Divisible]&]
%Y A329366 Intersection of A316476 and A328867.
%Y A329366 Heinz numbers of the partitions counted by A328871.
%Y A329366 Replacing "intersecting" with "relatively prime" gives A328677.
%Y A329366 Cf. A056239, A112798, A285573, A289509, A303362, A304713, A327393, A328671.
%K A329366 nonn
%O A329366 1,2
%A A329366 _Gus Wiseman_, Nov 12 2019