cp's OEIS Frontend

A325622 Number of integer partitions of n whose reciprocal factorial sum is the reciprocal of an integer.

%I A325622 #12 Feb 26 2025 06:35:16
%S A325622 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,
%T A325622 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,
%U A325622 12,11,10,10,12,14,11,10,9,10,12,10,15,14,11,10
%N A325622 Number of integer partitions of n whose reciprocal factorial sum is the reciprocal of an integer.
%C A325622 The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.
%e A325622 The initial terms count the following partitions:
%e A325622    1: (1)
%e A325622    2: (2)
%e A325622    3: (3)
%e A325622    4: (4)
%e A325622    4: (2,2)
%e A325622    5: (5)
%e A325622    6: (6)
%e A325622    6: (3,3)
%e A325622    7: (7)
%e A325622    8: (8)
%e A325622    8: (4,4)
%e A325622    9: (9)
%e A325622    9: (5,4)
%e A325622    9: (3,3,3)
%e A325622   10: (10)
%e A325622   10: (5,5)
%e A325622   11: (11)
%e A325622   11: (4,4,3)
%e A325622   11: (3,3,3,2)
%e A325622   12: (12)
%e A325622   12: (6,6)
%e A325622   12: (4,4,4)
%p A325622 f:= proc(n) nops(select(proc(t) local i; (1/add(1/i!,i=t))::integer end proc, combinat:-partition(n))) end proc:
%p A325622 map(f, [$1..70]); # _Robert Israel_, May 09 2024
%t A325622 Table[Length[Select[IntegerPartitions[n],IntegerQ[1/Total[1/(#!)]]&]],{n,30}]
%o A325622 (PARI) a(n) = my(c=0); forpart(v=n, if(numerator(sum(i=1, #v, 1/v[i]!))==1, c++)); c; \\ _Jinyuan Wang_, Feb 25 2025
%Y A325622 Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.
%Y A325622 Reciprocal factorial sum: A002966, A316854, A316857, A325618, A325620, A325623.
%K A325622 nonn
%O A325622 1,4
%A A325622 _Gus Wiseman_, May 13 2019
%E A325622 a(61)-a(70) from _Robert Israel_, May 09 2024
%E A325622 a(71)-a(80) from _Jinyuan Wang_, Feb 25 2025