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A325623 Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer.

%I A325623 #6 May 13 2019 08:12:24
%S A325623 1,2,3,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49,53,59,61,67,71,73,
%T A325623 77,79,83,89,97,101,103,107,109,113,121,125,127,131,137,139,149,151,
%U A325623 157,163,167,169,173,179,181,191,193,197,199,211,221,223,227,229
%N A325623 Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer.
%C A325623 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325623 The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.
%e A325623 The sequence of terms together with their prime indices begins:
%e A325623     1: {}
%e A325623     2: {1}
%e A325623     3: {2}
%e A325623     5: {3}
%e A325623     7: {4}
%e A325623     9: {2,2}
%e A325623    11: {5}
%e A325623    13: {6}
%e A325623    17: {7}
%e A325623    19: {8}
%e A325623    23: {9}
%e A325623    25: {3,3}
%e A325623    29: {10}
%e A325623    31: {11}
%e A325623    37: {12}
%e A325623    41: {13}
%e A325623    43: {14}
%e A325623    47: {15}
%e A325623    49: {4,4}
%e A325623    53: {16}
%t A325623 Select[Range[100],IntegerQ[1/Total[Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]!]]]&]
%Y A325623 Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.
%Y A325623 Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316857, A325619, A325621, A325622.
%K A325623 nonn
%O A325623 1,2
%A A325623 _Gus Wiseman_, May 13 2019