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A103264 Number of partitions of n into distinct parts prime to 3, 5 and 7. 0
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 6, 7, 8, 8, 9, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 23, 24, 26, 28, 31, 34, 37, 39, 42, 45, 49, 53, 56, 60, 64, 69, 75, 81, 86, 92, 98, 105, 113, 122, 130, 138, 147, 157, 168, 179, 191, 202, 215, 230, 246, 262, 279 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Table of n, a(n) for n=0..73.

FORMULA

G.f.: product_{k>0}((1+x^k)*(1+x^(15k))*(1+x^(21k))*(1+x^(35k)))/((1+x^(3k))*(1+x^(5k))*(1+x^(7k))*(1+x^(105k))).

a(n) ~ exp(4*Pi*sqrt(n/105)) / (sqrt(2) * 105^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 07 2015

EXAMPLE

a(19)=5 because 19 = 17 + 2 = 16 + 2 + 1 = 13 + 4 + 2 = 11 + 8.

MAPLE

series(product((1+x^k)*(1+x^(15*k))*(1+x^(21*k))*(1+x^(35*k)))/((1+x^(3*k))*(1+x^(5*k))*(1+x^(7*k))*(1+x^(105*k))), k=1..100), x=0, 100);

MATHEMATICA

CoefficientList[ Series[ Product[(1 + x^k)(1 + x^(15k))(1 + x^(21k))(1 + x^(35k))/((1 + x^(3k))(1 + x^(5k))(1 + x^(7k))(1 + x^(105k))), {k, 100}], {x, 0, 73}], x] (* Robert G. Wilson v, Feb 22 2005 *)

CROSSREFS

Sequence in context: A281687 A033270 A285507 * A225644 A225633 A060960

Adjacent sequences:  A103261 A103262 A103263 * A103265 A103266 A103267

KEYWORD

nonn

AUTHOR

Noureddine Chair, Feb 21 2005

EXTENSIONS

More terms from Robert G. Wilson v, Feb 22 2005

STATUS

approved

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Last modified February 26 13:29 EST 2021. Contains 341632 sequences. (Running on oeis4.)