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A225245 Number of partitions of n into distinct squarefree divisors of n. 9
1, 1, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 4, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 3, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 3, 1, 1, 0, 0, 1, 3, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 2, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

a(n) <= A033630(n);

a(n) = A033630(n) iff n is squarefree: a(A005117(n)) = A033630(A005117(n));

a(A225353(n)) = 0; a(A225354(n)) > 0.

LINKS

Reinhard Zumkeller and Alois P. Heinz, Table of n, a(n) for n = 0..10000 (5000 terms from Reinhard Zumkeller)

FORMULA

a(n) = [x^n] Product_{d|n, mu(d) != 0} (1 + x^d), where mu() is the Moebius function (A008683). - Ilya Gutkovskiy, Jul 26 2017

EXAMPLE

a(2*3)     = a(6)  = #{6, 3+2+1} = 2;

a(2*2*3)   = a(12) = #{6+3+2+1} = 1;

a(2*3*5)   = a(30) = #{30, 15+10+5, 15+10+3+2, 15+6+5+3+1} = 4;

a(2*2*3*5) = a(60) = #{30+15+10+5, 30+15+10+3+2, 30+15+6+5+3+1} = 3;

a(2*3*7)   = a(42) = #{42, 21+14+7, 21+14+6+1} = 3;

a(2*2*3*7) = a(84) = #{42+21+14+7, 42+21+14+6+1} = 2.

PROG

(Haskell)

a225245 n = p (a206778_row n) n where

   p _      0 = 1

   p []     _ = 0

   p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m

CROSSREFS

Cf. A005117, A008683, A033630, A206778, A008966, A225244, A087188, A225353.

Sequence in context: A255318 A249223 A115953 * A204770 A333382 A143379

Adjacent sequences:  A225242 A225243 A225244 * A225246 A225247 A225248

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2013

STATUS

approved

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Last modified May 11 18:21 EDT 2021. Contains 343808 sequences. (Running on oeis4.)