cp's OEIS Frontend

A324929 Numbers whose product of prime indices is even.

%I A324929 #9 Mar 22 2019 05:24:57
%S A324929 3,6,7,9,12,13,14,15,18,19,21,24,26,27,28,29,30,33,35,36,37,38,39,42,
%T A324929 43,45,48,49,51,52,53,54,56,57,58,60,61,63,65,66,69,70,71,72,74,75,76,
%U A324929 77,78,79,81,84,86,87,89,90,91,93,95,96,98,99,101,102,104
%N A324929 Numbers whose product of prime indices is even.
%C A324929 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, with product A003963(n).
%C A324929 Also Heinz numbers of integer partitions whose product of parts is even (counted by A047967), where the Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k).
%e A324929 The sequence of terms together with their prime indices begins:
%e A324929    3: {2}
%e A324929    6: {1,2}
%e A324929    7: {4}
%e A324929    9: {2,2}
%e A324929   12: {1,1,2}
%e A324929   13: {6}
%e A324929   14: {1,4}
%e A324929   15: {2,3}
%e A324929   18: {1,2,2}
%e A324929   19: {8}
%e A324929   21: {2,4}
%e A324929   24: {1,1,1,2}
%e A324929   26: {1,6}
%e A324929   27: {2,2,2}
%e A324929   28: {1,1,4}
%e A324929   29: {10}
%e A324929   30: {1,2,3}
%e A324929   33: {2,5}
%e A324929   35: {3,4}
%e A324929   36: {1,1,2,2}
%t A324929 Select[Range[100],EvenQ[Times@@PrimePi/@If[#==1,{},FactorInteger[#]][[All,1]]]&]
%o A324929 (PARI) isok(n) = my(f=factor(n)[,1]); !(prod(k=1, #f, primepi(f[k])) % 2); \\ _Michel Marcus_, Mar 22 2019
%Y A324929 Cf. A000720, A001222, A003963, A005087, A033844, A047967, A066208, A112798, A257992, A318400, A324927.
%K A324929 nonn
%O A324929 1,1
%A A324929 _Gus Wiseman_, Mar 21 2019