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 A325622 Number of integer partitions of n whose reciprocal factorial sum is the reciprocal of an integer. 7
 1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 3, 3, 2, 2, 3, 3, 3, 5, 4, 4, 3, 3, 4, 6, 3, 4, 5, 5, 5, 6, 3, 7, 6, 5, 6, 6, 6, 5, 6, 8, 5, 7, 5, 4, 8, 7, 7, 7, 7, 9, 9, 9, 10, 12, 6, 12, 8, 10, 7, 14, 10, 8, 11, 11, 12, 11, 10, 10, 12, 14 (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..70. EXAMPLE The initial terms count the following partitions: 1: (1) 2: (2) 3: (3) 4: (4) 4: (2,2) 5: (5) 6: (6) 6: (3,3) 7: (7) 8: (8) 8: (4,4) 9: (9) 9: (5,4) 9: (3,3,3) 10: (10) 10: (5,5) 11: (11) 11: (4,4,3) 11: (3,3,3,2) 12: (12) 12: (6,6) 12: (4,4,4) MAPLE f:= proc(n) nops(select(proc(t) local i; (1/add(1/i!, i=t))::integer end proc, combinat:-partition(n))) end proc: map(f, [\$1..70]); # Robert Israel, May 09 2024 MATHEMATICA Table[Length[Select[IntegerPartitions[n], IntegerQ[1/Total[1/(#!)]]&]], {n, 30}] CROSSREFS Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616. Reciprocal factorial sum: A002966, A316854, A316857, A325618, A325620, A325623. Sequence in context: A194509 A054716 A261641 * A060145 A358997 A373461 Adjacent sequences: A325619 A325620 A325621 * A325623 A325624 A325625 KEYWORD nonn,more AUTHOR Gus Wiseman, May 13 2019 EXTENSIONS a(61)-a(70) from Robert Israel, May 09 2024 STATUS approved

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Last modified September 18 14:24 EDT 2024. Contains 376000 sequences. (Running on oeis4.)