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A168657 Number of partitions of n such that the number of parts is divisible by the smallest part. 4
1, 1, 2, 4, 6, 8, 12, 17, 25, 34, 48, 64, 87, 114, 151, 198, 258, 332, 428, 546, 695, 879, 1108, 1388, 1737, 2159, 2680, 3312, 4082, 5009, 6138, 7492, 9126, 11081, 13429, 16228, 19575, 23547, 28277, 33879, 40520, 48354, 57615, 68509, 81337, 96388, 114055 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: Sum( Sum_{d|n} x^(n*d)/Product( 1-x^k, k=1..n-1 ), n=1..infinity ).

MAPLE

b:= proc(n, i, t) option remember;

      `if` (n<1, 0, `if` (i=1, 1, `if` (i<1, 0,

      `if` (irem(n, i)=0 and irem(t+n/i, i)=0, 1, 0)+

            add(b(n-i*j, i-1, t+j), j=0..n/i))))

    end:

a:= n-> b(n, n, 0):

seq (a(n), n=1..60);  # Alois P. Heinz, May 24 2012

MATHEMATICA

b[n_, i_, t_] := b[n, i, t] = If[n<1, 0, If[i==1, 1, If[i<1, 0, If [Mod[n, i]==0 && Mod[t+n/i, i]==0, 1, 0] + Sum[b[n-i*j, i-1, t+j], {j, 0, n/i}]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 1, 60}] (* Jean-Fran├žois Alcover, Jul 01 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A079501, A168655, A168656.

Sequence in context: A181821 A241882 A238626 * A240498 A081954 A096903

Adjacent sequences:  A168654 A168655 A168656 * A168658 A168659 A168660

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Dec 02 2009

STATUS

approved

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Last modified July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)