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A325618 Numbers m such that there exists an integer partition of m whose reciprocal factorial sum is 1.

%I A325618 #13 Jul 20 2021 23:48:55
%S A325618 1,4,11,18,24,31,37,44,45,50,52,57,58,65,66,70,71,73,76,78,79,83,86,
%T A325618 87,89,91,92,94,96,97,99,100,102,104,107,108,109,110,112,113,114,115,
%U A325618 117,118,119,120,121,122,123,125,126,127,128,130,131
%N A325618 Numbers m such that there exists an integer partition of m whose reciprocal factorial sum is 1.
%C A325618 The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.
%C A325618 Conjecture: 137 is the greatest integer not in this sequence. - _Charlie Neder_, May 14 2019
%H A325618 Charlie Neder, <a href="/A325618/b325618.txt">Table of n, a(n) for n = 1..1000</a>
%e A325618 The sequence of terms together with an integer partition of each whose reciprocal factorial sum is 1 begins:
%e A325618    1: (1)
%e A325618    4: (2,2)
%e A325618   11: (3,3,3,2)
%e A325618   18: (3,3,3,3,3,3)
%e A325618   24: (4,4,4,4,3,3,2)
%e A325618   31: (4,4,4,4,3,3,3,3,3)
%e A325618   37: (4,4,4,4,4,4,4,4,3,2)
%e A325618   44: (4,4,4,4,4,4,4,4,3,3,3,3)
%e A325618   45: (5,5,5,5,5,4,4,4,3,3,2)
%e A325618   50: (4,4,4,4,4,4,4,4,4,4,4,4,2)
%Y A325618 Factorial numbers: A000142, A002982, A007489, A011371, A022559, A064986, A115627, A284605, A325616.
%Y A325618 Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316855, A325619, A325620, A325621, A325622, A325623, A325624.
%K A325618 nonn
%O A325618 1,2
%A A325618 _Gus Wiseman_, May 13 2019
%E A325618 a(11)-a(55) from _Charlie Neder_, May 14 2019