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A325618 Numbers n such that there exists an integer partition of n whose reciprocal factorial sum is 1. 11
1, 4, 11, 18, 24, 31, 37, 44, 45, 50, 52, 57, 58, 65, 66, 70, 71, 73, 76, 78, 79, 83, 86, 87, 89, 91, 92, 94, 96, 97, 99, 100, 102, 104, 107, 108, 109, 110, 112, 113, 114, 115, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 130, 131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Conjecture: 137 is the greatest integer not in this sequence. - Charlie Neder, May 14 2019

LINKS

Charlie Neder, Table of n, a(n) for n = 1..1000

EXAMPLE

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

   1: (1)

   4: (2,2)

  11: (3,3,3,2)

  18: (3,3,3,3,3,3)

  24: (4,4,4,4,3,3,2)

  31: (4,4,4,4,3,3,3,3,3)

  37: (4,4,4,4,4,4,4,4,3,2)

  44: (4,4,4,4,4,4,4,4,3,3,3,3)

  45: (5,5,5,5,5,4,4,4,3,3,2)

  50: (4,4,4,4,4,4,4,4,4,4,4,4,2)

CROSSREFS

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

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

Sequence in context: A133725 A050395 A059771 * A043409 A030610 A003327

Adjacent sequences:  A325615 A325616 A325617 * A325619 A325620 A325621

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 13 2019

EXTENSIONS

a(11)-a(55) from Charlie Neder, May 14 2019

STATUS

approved

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Last modified April 17 02:18 EDT 2021. Contains 343059 sequences. (Running on oeis4.)