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A286220 Number of partitions of n into distinct parts with an odd number of distinct prime divisors. 3
1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 3, 5, 5, 6, 7, 7, 10, 9, 12, 12, 15, 15, 18, 19, 22, 24, 26, 30, 32, 36, 40, 43, 49, 52, 58, 63, 69, 76, 81, 91, 96, 108, 114, 127, 135, 148, 159, 173, 186, 202, 217, 234, 253, 271, 293, 313, 339, 361, 390, 416, 449, 478, 514, 547, 588, 625, 671, 714, 763, 815, 867 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..70.

Eric Weisstein's World of Mathematics, Distinct Prime Factors

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} (1 + x^A030230(k)).

EXAMPLE

a(9) = 4 because we have [9], [7, 2], [5, 4] and [4, 3, 2].

MATHEMATICA

nmax = 70; CoefficientList[Series[Product[1 + Boole[OddQ[PrimeNu[k]]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A030230, A285799, A286221.

Sequence in context: A266755 A029142 A054685 * A246581 A143619 A029141

Adjacent sequences:  A286217 A286218 A286219 * A286221 A286222 A286223

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 04 2017

STATUS

approved

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Last modified April 23 14:15 EDT 2019. Contains 322386 sequences. (Running on oeis4.)