OFFSET
0,8
COMMENTS
Also the number of integer partitions of n containing 1 whose product is a multiple of n. Without requiring a 1 we get A057568.
EXAMPLE
The a(5) = 1 through a(11) = 14 partitions:
(3,2) . (4,2,1) (3,3,2) (5,4) . (8,3)
(2,2,2,1) (3,3,1,1) (5,2,2) (4,4,3)
(5,2,1,1) (6,3,2)
(6,4,1)
(4,3,2,2)
(4,3,3,1)
(6,2,2,1)
(3,2,2,2,2)
(3,3,2,2,1)
(4,3,2,1,1)
(6,2,1,1,1)
(3,2,2,2,1,1)
(4,3,1,1,1,1)
(3,2,2,1,1,1,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Divisible[Times@@#, n+1]&]], {n, 0, 30}]
PROG
(PARI) a(n) = my(nb=0); forpart(p=n, if (!(vecprod(Vec(p)) % (n+1)), nb++)); nb; \\ Michel Marcus, Jan 21 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 18 2025
STATUS
approved