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A024994 Number of periodic partitions of n: each part occurs more than once and the same number of times. 6
0, 1, 1, 2, 1, 4, 1, 4, 3, 5, 1, 10, 1, 7, 6, 10, 1, 16, 1, 17, 8, 14, 1, 31, 4, 20, 11, 31, 1, 48, 1, 42, 15, 40, 9, 79, 1, 56, 21, 87, 1, 111, 1, 105, 41, 106, 1, 185, 6, 157, 41, 187, 1, 254, 16, 259, 57, 258, 1, 425, 1, 342, 92, 432, 22, 557, 1, 554, 107, 627, 1, 875, 1, 762, 175, 922, 18, 1173 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = Sum(q(k)), where k divides n, k < n, where q(n) = A000009(n), distinct partitions. - Alford Arnold

EXAMPLE

E.g. 6 = 1+1+1+1+1+1 = 2+2+2 = 3+3 = 2+1+2+1, so a(6)=4.

MAPLE

with(numtheory):

b:= proc(n) option remember; `if`(n=0, 1, add(add(

     `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)

    end:

a:= n-> add(b(d), d=divisors(n) minus {n}):

seq(a(n), n=1..100);  # Alois P. Heinz, Jul 11 2016

MATHEMATICA

b[n_] := b[n] = If[n == 0, 1, Sum[Sum[If[OddQ[d], d, 0], {d, Divisors[j]}]* b[n-j], {j, 1, n}]/n]; a[n_] := Sum[b[d], {d, Divisors[n] ~Complement~ {n}}]; Table[a[n], {n, 1, 100}] (* Jean-Fran├žois Alcover, Jan 25 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A000009, A047966.

Sequence in context: A319711 A319713 A063717 * A243329 A051953 A079277

Adjacent sequences:  A024991 A024992 A024993 * A024995 A024996 A024997

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

a(1) set to 0 by Alois P. Heinz, Jul 11 2016

STATUS

approved

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Last modified September 20 16:44 EDT 2019. Contains 327242 sequences. (Running on oeis4.)