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A325621 Heinz numbers of integer partitions whose reciprocal factorial sum is an integer.

%I A325621 #6 May 13 2019 08:12:17
%S A325621 1,2,4,8,9,16,18,32,36,64,72,81,128,144,162,256,288,324,375,512,576,
%T A325621 648,729,750,1024,1152,1296,1458,1500,2048,2304,2592,2916,3000,3375,
%U A325621 4096,4608,5184,5832,6000,6561,6750,8192,9216,10368,11664,12000,13122,13500
%N A325621 Heinz numbers of integer partitions whose reciprocal factorial sum is an integer.
%C A325621 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325621 The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.
%e A325621 The sequence of terms together with their prime indices begins:
%e A325621       1: {}
%e A325621       2: {1}
%e A325621       4: {1,1}
%e A325621       8: {1,1,1}
%e A325621       9: {2,2}
%e A325621      16: {1,1,1,1}
%e A325621      18: {1,2,2}
%e A325621      32: {1,1,1,1,1}
%e A325621      36: {1,1,2,2}
%e A325621      64: {1,1,1,1,1,1}
%e A325621      72: {1,1,1,2,2}
%e A325621      81: {2,2,2,2}
%e A325621     128: {1,1,1,1,1,1,1}
%e A325621     144: {1,1,1,1,2,2}
%e A325621     162: {1,2,2,2,2}
%e A325621     256: {1,1,1,1,1,1,1,1}
%e A325621     288: {1,1,1,1,1,2,2}
%e A325621     324: {1,1,2,2,2,2}
%e A325621     375: {2,3,3,3}
%e A325621     512: {1,1,1,1,1,1,1,1,1}
%t A325621 Select[Range[1000],IntegerQ[Total[Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]!]]]&]
%Y A325621 Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.
%Y A325621 Reciprocal factorial sum: A002966, A058360, A316856, A325619, A325620, A325623.
%K A325621 nonn
%O A325621 1,2
%A A325621 _Gus Wiseman_, May 13 2019