A325623 - OEIS

%I #6 May 13 2019 08:12:24

%S 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 77,79,83,89,97,101,103,107,109,113,121,125,127,131,137,139,149,151,

%U 157,163,167,169,173,179,181,191,193,197,199,211,221,223,227,229

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

%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

%C The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.

%e The sequence of terms together with their prime indices begins:

%e     1: {}

%e     2: {1}

%e     3: {2}

%e     5: {3}

%e     7: {4}

%e     9: {2,2}

%e    11: {5}

%e    13: {6}

%e    17: {7}

%e    19: {8}

%e    23: {9}

%e    25: {3,3}

%e    29: {10}

%e    31: {11}

%e    37: {12}

%e    41: {13}

%e    43: {14}

%e    47: {15}

%e    49: {4,4}

%e    53: {16}

%t Select[Range[100],IntegerQ[1/Total[Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]!]]]&]

%Y Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.

%Y Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316857, A325619, A325621, A325622.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 13 2019