A325618 - OEIS

%I #13 Jul 20 2021 23:48:55

%S 1,4,11,18,24,31,37,44,45,50,52,57,58,65,66,70,71,73,76,78,79,83,86,

%T 87,89,91,92,94,96,97,99,100,102,104,107,108,109,110,112,113,114,115,

%U 117,118,119,120,121,122,123,125,126,127,128,130,131

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

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

%C Conjecture: 137 is the greatest integer not in this sequence. - _Charlie Neder_, May 14 2019

%H Charlie Neder, <a href="/A325618/b325618.txt">Table of n, a(n) for n = 1..1000</a>

%e The sequence of terms together with an integer partition of each whose reciprocal factorial sum is 1 begins:

%e    1: (1)

%e    4: (2,2)

%e   11: (3,3,3,2)

%e   18: (3,3,3,3,3,3)

%e   24: (4,4,4,4,3,3,2)

%e   31: (4,4,4,4,3,3,3,3,3)

%e   37: (4,4,4,4,4,4,4,4,3,2)

%e   44: (4,4,4,4,4,4,4,4,3,3,3,3)

%e   45: (5,5,5,5,5,4,4,4,3,3,2)

%e   50: (4,4,4,4,4,4,4,4,4,4,4,4,2)

%Y Factorial numbers: A000142, A002982, A007489, A011371, A022559, A064986, A115627, A284605, A325616.

%Y Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316855, A325619, A325620, A325621, A325622, A325623, A325624.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 13 2019

%E a(11)-a(55) from _Charlie Neder_, May 14 2019