cp's OEIS Frontend

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

%I A325701 #5 May 17 2019 22:06:56
%S A325701 1,9,25,49,77,121,125,169,221,245,289,323,343,361,375,437,529,841,899,
%T A325701 961,1331,1369,1517,1681,1763,1849,1859,2021,2197,2209,2401,2773,2809,
%U A325701 2873,3127,3481,3721,3757,4087,4489,4757,4913,5041,5183,5329,5929,6137,6241
%N A325701 Nonprime Heinz numbers of integer partitions whose reciprocal factorial sum is the reciprocal of an integer.
%C A325701 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325701 The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.
%e A325701 The sequence of terms together with their prime indices begins:
%e A325701      1: {}
%e A325701      9: {2,2}
%e A325701     25: {3,3}
%e A325701     49: {4,4}
%e A325701     77: {4,5}
%e A325701    121: {5,5}
%e A325701    125: {3,3,3}
%e A325701    169: {6,6}
%e A325701    221: {6,7}
%e A325701    245: {3,4,4}
%e A325701    289: {7,7}
%e A325701    323: {7,8}
%e A325701    343: {4,4,4}
%e A325701    361: {8,8}
%e A325701    375: {2,3,3,3}
%e A325701    437: {8,9}
%e A325701    529: {9,9}
%e A325701    841: {10,10}
%e A325701    899: {10,11}
%e A325701    961: {11,11}
%e A325701 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 A325701 Select[Range[1000],!PrimeQ[#]&&IntegerQ[1/Total[Cases[FactorInteger[#],{p_,k_}:>k/PrimePi[p]!]]]&]
%Y A325701 Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.
%Y A325701 Reciprocal factorial sum: A002966, A316854, A316857, A325618, A325620, A325622, A325623.
%K A325701 nonn
%O A325701 1,2
%A A325701 _Gus Wiseman_, May 17 2019