A325621 - OEIS

%I #6 May 13 2019 08:12:17

%S 1,2,4,8,9,16,18,32,36,64,72,81,128,144,162,256,288,324,375,512,576,

%T 648,729,750,1024,1152,1296,1458,1500,2048,2304,2592,2916,3000,3375,

%U 4096,4608,5184,5832,6000,6561,6750,8192,9216,10368,11664,12000,13122,13500

%N Heinz numbers of integer partitions whose reciprocal factorial sum is 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       4: {1,1}

%e       8: {1,1,1}

%e       9: {2,2}

%e      16: {1,1,1,1}

%e      18: {1,2,2}

%e      32: {1,1,1,1,1}

%e      36: {1,1,2,2}

%e      64: {1,1,1,1,1,1}

%e      72: {1,1,1,2,2}

%e      81: {2,2,2,2}

%e     128: {1,1,1,1,1,1,1}

%e     144: {1,1,1,1,2,2}

%e     162: {1,2,2,2,2}

%e     256: {1,1,1,1,1,1,1,1}

%e     288: {1,1,1,1,1,2,2}

%e     324: {1,1,2,2,2,2}

%e     375: {2,3,3,3}

%e     512: {1,1,1,1,1,1,1,1,1}

%t Select[Range[1000],IntegerQ[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, A058360, A316856, A325619, A325620, A325623.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 13 2019