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A171565 Number of partitions of n into odd divisors of n. 7
1, 1, 1, 2, 1, 2, 3, 2, 1, 5, 3, 2, 5, 2, 3, 14, 1, 2, 12, 2, 5, 18, 3, 2, 9, 7, 3, 23, 5, 2, 54, 2, 1, 26, 3, 26, 35, 2, 3, 30, 9, 2, 72, 2, 5, 286, 3, 2, 17, 9, 18, 38, 5, 2, 93, 38, 9, 42, 3, 2, 275, 2, 3, 493, 1, 44, 108, 2, 5, 50, 110, 2, 117, 2, 3, 698, 5, 50, 126, 2, 17, 239, 3, 2, 375, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(2*n+1) = A018818(2*n+1), a(A005408(n))=A018818(A005408(n));

a(2^k) = 1, a(A000079(n))=1;

for odd primes p: a(p*2^k) = 2^k + 1,

especially for n>1: a(A000040(n))=2, a(A100484(n))=3, a(A001749(n))=5.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = f(n,n,1) with f(n,m,k) = if k<=m then f(n,m,k+2)+f(n,m-k,k)*0^(n mod k) else 0^m.

MAPLE

with(numtheory):

a:= proc(n) option remember; local b, l; l, b:= sort(

      [select(x-> is(x:: odd), divisors(n))[]]),

      proc(m, i) option remember; `if`(m=0, 1, `if`(i<1, 0,

        b(m, i-1)+`if`(l[i]>m, 0, b(m-l[i], i))))

      end; b(n, nops(l))

    end:

seq(a(n), n=0..100);  # Alois P. Heinz, Mar 30 2017

MATHEMATICA

a[0] = 1; a[n_] := a[n] = Module[{b, l}, l = Select[Divisors[n], OddQ]; b[m_, i_] := b[m, i] = If[m == 0, 1, If[i < 1, 0, b[m, i-1] + If[l[[i]] > m, 0, b[m - l[[i]], i]]]]; b[n, Length[l]]];

Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Apr 11 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A038550, A065091.

Sequence in context: A101050 A128979 A190167 * A328266 A115116 A141662

Adjacent sequences:  A171562 A171563 A171564 * A171566 A171567 A171568

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Dec 11 2009

STATUS

approved

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)