cp's OEIS Frontend

A324758 Heinz numbers of integer partitions containing no prime indices of the parts.

%I A324758 #6 Mar 18 2019 08:14:17
%S A324758 1,2,3,4,5,7,8,9,10,11,13,16,17,19,20,21,22,23,25,27,29,31,32,33,34,
%T A324758 35,37,40,41,43,44,46,47,49,50,51,53,57,59,61,62,63,64,65,67,68,71,73,
%U A324758 77,79,80,81,82,83,85,87,88,89,91,92,93,94,95,97,99,100,101
%N A324758 Heinz numbers of integer partitions containing no prime indices of the parts.
%C A324758 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. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%C A324758 These could be described as anti-transitive numbers (cf. A290822), as they are numbers x such that if prime(y) divides x and prime(z) divides y, then prime(z) does not divide x.
%C A324758 Also numbers n such that A003963(n) is coprime to n.
%e A324758 The sequence of terms together with their prime indices begins:
%e A324758    1: {}
%e A324758    2: {1}
%e A324758    3: {2}
%e A324758    4: {1,1}
%e A324758    5: {3}
%e A324758    7: {4}
%e A324758    8: {1,1,1}
%e A324758    9: {2,2}
%e A324758   10: {1,3}
%e A324758   11: {5}
%e A324758   13: {6}
%e A324758   16: {1,1,1,1}
%e A324758   17: {7}
%e A324758   19: {8}
%e A324758   20: {1,1,3}
%e A324758   21: {2,4}
%e A324758   22: {1,5}
%e A324758   23: {9}
%e A324758   25: {3,3}
%e A324758   27: {2,2,2}
%t A324758 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A324758 Select[Range[100],Intersection[primeMS[#],Union@@primeMS/@primeMS[#]]=={}&]
%Y A324758 The subset version is A324741, with maximal case A324743. The strict integer partition version is A324751. The integer partition version is A324756. An infinite version is A324695.
%Y A324758 Cf. A000720, A001221, A001462, A007097, A056239, A112798, A276625, A289509, A290822, A304360, A306844, A324742, A324753, A324764.
%K A324758 nonn
%O A324758 1,2
%A A324758 _Gus Wiseman_, Mar 17 2019