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