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 A067538 Number of partitions of n in which the number of parts divides n. 40
 1, 2, 2, 4, 2, 8, 2, 11, 9, 14, 2, 46, 2, 24, 51, 66, 2, 126, 2, 202, 144, 69, 2, 632, 194, 116, 381, 756, 2, 1707, 2, 1417, 956, 316, 2043, 5295, 2, 511, 2293, 9151, 2, 10278, 2, 8409, 14671, 1280, 2, 36901, 8035, 21524, 11614, 25639, 2, 53138, 39810, 85004 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also sum of p(n,d) over the divisors d of n, where p(n,m) is the count of partitions of n in exactly m parts. - Wouter Meeussen, Jun 07 2009 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 (first 500 terms from Wouter Meeussen) Eric W. Weisstein, Partition Function P Wikipedia, Integer Partition FORMULA a(p) = 2 for all primes p. EXAMPLE a(3)=2 because 3 is a prime; a(4)=4 because the five partitions of 4 are {4}, {3, 1}, {2, 2}, {2, 1, 1}, {1, 1, 1, 1}, and the number of parts in each of them divides 4 except for {2, 1, 1}. MATHEMATICA Do[p = IntegerPartitions[n]; l = Length[p]; c = 0; k = 1; While[k < l + 1, If[ IntegerQ[ n/Length[ p[[k]] ]], c++ ]; k++ ]; Print[c], {n, 1, 57}, All] p[n_, k_]:=p[n, k]=p[n-1, k-1]+p[n-k, k]; p[n_, k_]:=0/; k>n; p[n_, n_]:=1; p[n_, 0]:=0 Table[Plus @@ (p[n, # ]&/ @ Divisors[n]), {n, 36}] (* Wouter Meeussen, Jun 07 2009 *) Table[Count[IntegerPartitions[n], q_ /; IntegerQ[Mean[q]]], {n, 50}]  (*Clark Kimberling, Apr 23 2019 *) PROG (PARI) a(n) = {my(nb = 0); forpart(p=n, if ((vecsum(Vec(p)) % #p) == 0, nb++); ); nb; } \\ Michel Marcus, Jul 03 2018 CROSSREFS Cf. A000005, A000041, A143773, A298422, A298423, A298426. Sequence in context: A100577 A018818 A157019 * A305982 A304102 A096154 Adjacent sequences:  A067535 A067536 A067537 * A067539 A067540 A067541 KEYWORD easy,nonn AUTHOR Naohiro Nomoto, Jan 27 2002 EXTENSIONS Extended by Robert G. Wilson v, Oct 16 2002 STATUS approved

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Last modified July 23 11:44 EDT 2019. Contains 325254 sequences. (Running on oeis4.)