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A325701 Nonprime Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer. 0

%I

%S 1,9,25,49,77,121,125,169,221,245,289,323,343,361,375,437,529,841,899,

%T 961,1331,1369,1517,1681,1763,1849,1859,2021,2197,2209,2401,2773,2809,

%U 2873,3127,3481,3721,3757,4087,4489,4757,4913,5041,5183,5329,5929,6137,6241

%N Nonprime 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 9: {2,2}

%e 25: {3,3}

%e 49: {4,4}

%e 77: {4,5}

%e 121: {5,5}

%e 125: {3,3,3}

%e 169: {6,6}

%e 221: {6,7}

%e 245: {3,4,4}

%e 289: {7,7}

%e 323: {7,8}

%e 343: {4,4,4}

%e 361: {8,8}

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

%e 437: {8,9}

%e 529: {9,9}

%e 841: {10,10}

%e 899: {10,11}

%e 961: {11,11}

%e For example, the sequence contains 245 because the prime indices of 245 are {3,4,4}, with reciprocal sum 1/6 + 1/24 + 1/24 = 1/4.

%t Select[Range[1000],!PrimeQ[#]&&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, A316854, A316857, A325618, A325620, A325622, A325623.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 17 2019

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Last modified April 18 14:58 EDT 2021. Contains 343089 sequences. (Running on oeis4.)