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 A057568 Number of partitions of n where n divides the product of the parts. 28
 1, 1, 1, 2, 1, 2, 1, 6, 5, 5, 1, 22, 1, 11, 23, 80, 1, 113, 1, 150, 85, 45, 1, 737, 226, 84, 809, 726, 1, 1787, 1, 4261, 735, 260, 1925, 9567, 1, 437, 1877, 16402, 1, 14630, 1, 9861, 33057, 1152, 1, 102082, 19393, 57330, 10159, 30706, 1, 207706, 47927, 200652 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 (terms n=1..73 from Antti Karttunen) EXAMPLE From Gus Wiseman, Jul 04 2019: (Start) The a(1) = 1 through a(9) = 5 partitions are the following. The Heinz numbers of these partitions are given by A326149.   (1)  (2)  (3)  (4)   (5)  (6)    (7)  (8)      (9)                  (22)       (321)       (44)     (63)                                         (422)    (333)                                         (2222)   (3321)                                         (4211)   (33111)                                         (22211) (End) MAPLE b:= proc(n, i, t) option remember; `if`(n=0,       `if`(t=1, 1, 0), `if`(i<1, 0, b(n, i-1, t)+       `if`(i>n, 0, b(n-i, min(i, n-i), t/igcd(i, t)))))     end: a:= n-> `if`(isprime(n), 1, b(n\$3)): seq(a(n), n=1..70);  # Alois P. Heinz, Dec 20 2017 MATHEMATICA Table[Length[Select[IntegerPartitions[n], Divisible[Times@@#, n]&]], {n, 20}] (* Gus Wiseman, Jul 04 2019 *) PROG (Scheme) ;; This is a naive algorithm that scans over all partitions of each n. For fold_over_partitions_of see A000793. (define (A057568 n) (let ((z (list 0))) (fold_over_partitions_of n 1 * (lambda (partprod) (if (zero? (modulo partprod n)) (set-car! z (+ 1 (car z)))))) (car z))) ;; Antti Karttunen, Dec 20 2017 CROSSREFS Cf. A028422, A057567, A096276, A113309, A114324, A318950, A319000, A319005, A326149, A326152. Sequence in context: A327899 A276157 A169593 * A220587 A195962 A046749 Adjacent sequences:  A057565 A057566 A057567 * A057569 A057570 A057571 KEYWORD nonn AUTHOR Leroy Quet, Oct 04 2000 EXTENSIONS More terms from James A. Sellers, Oct 09 2000 STATUS approved

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Last modified June 4 04:39 EDT 2020. Contains 334815 sequences. (Running on oeis4.)