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A325620 Number of integer partitions of n whose reciprocal factorial sum is an integer. 7
1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 14, 14, 15, 16, 18, 19, 20, 22, 24, 25, 26, 28, 31, 33, 34, 36, 39, 41, 43, 45, 49, 52, 54, 57, 61, 65, 68, 71, 76, 80, 84, 88, 93, 98, 103, 107, 113 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

The initial terms count the following partitions:

  1: (1)

  2: (1,1)

  3: (1,1,1)

  4: (2,2)

  4: (1,1,1,1)

  5: (2,2,1)

  5: (1,1,1,1,1)

  6: (2,2,1,1)

  6: (1,1,1,1,1,1)

  7: (2,2,1,1,1)

  7: (1,1,1,1,1,1,1)

  8: (2,2,2,2)

  8: (2,2,1,1,1,1)

  8: (1,1,1,1,1,1,1,1)

  9: (2,2,2,2,1)

  9: (2,2,1,1,1,1,1)

  9: (1,1,1,1,1,1,1,1,1)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], IntegerQ[Total[1/(#!)]]&]], {n, 30}]

CROSSREFS

Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.

Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316856, A325618, A325621, A325622.

Sequence in context: A169992 A025775 A169993 * A270433 A169994 A169995

Adjacent sequences:  A325617 A325618 A325619 * A325621 A325622 A325623

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, May 13 2019

STATUS

approved

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Last modified September 27 10:35 EDT 2020. Contains 337380 sequences. (Running on oeis4.)