cp's OEIS Frontend

A324561 Numbers with at least one prime index equal to 0, 1, or 4 modulo 5.

%I A324561 #7 Mar 07 2019 19:56:58
%S A324561 2,4,6,7,8,10,11,12,13,14,16,18,20,21,22,23,24,26,28,29,30,31,32,33,
%T A324561 34,35,36,38,39,40,42,43,44,46,47,48,49,50,52,53,54,55,56,58,60,62,63,
%U A324561 64,65,66,67,68,69,70,71,72,73,74,76,77,78,80,82,84,86,87
%N A324561 Numbers with at least one prime index equal to 0, 1, or 4 modulo 5.
%C A324561 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 A324561 Also Heinz numbers of the integer partitions counted by A039900. The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
%e A324561 The sequence of terms together with their prime indices begins:
%e A324561    2: {1}
%e A324561    4: {1,1}
%e A324561    6: {1,2}
%e A324561    7: {4}
%e A324561    8: {1,1,1}
%e A324561   10: {1,3}
%e A324561   11: {5}
%e A324561   12: {1,1,2}
%e A324561   13: {6}
%e A324561   14: {1,4}
%e A324561   16: {1,1,1,1}
%e A324561   18: {1,2,2}
%e A324561   20: {1,1,3}
%e A324561   21: {2,4}
%e A324561   22: {1,5}
%e A324561   23: {9}
%e A324561   24: {1,1,1,2}
%p A324561 with(numtheory):
%p A324561 q:= n-> is(irem(pi(min(factorset(n))), 5) in {0, 1, 4}):
%p A324561 select(q, [$2..100])[];  # _Alois P. Heinz_, Mar 07 2019
%t A324561 Select[Range[100],Intersection[Mod[If[#==1,{},PrimePi/@First/@FactorInteger[#]],5],{0,1,4}]!={}&]
%Y A324561 Cf. A008854, A039900, A055396, A056239, A061395, A106529, A112798.
%Y A324561 Cf. A324519, A324521, A324522, A324560, A324561, A324562.
%K A324561 nonn
%O A324561 1,1
%A A324561 _Gus Wiseman_, Mar 06 2019