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A117221 Number of partitions of 3-smooth numbers. 6
1, 2, 3, 5, 11, 22, 30, 77, 231, 385, 1575, 3010, 8349, 17977, 147273, 386155, 1741630, 5392783, 18004327, 118114304, 483502844, 4351078600, 22540654445, 129913904637, 1987276856363, 15285151248481, 133978259344888, 365749566870782, 3925922161489422, 49005643635237875 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..100

FORMULA

a(n) = A000041(A003586(n)).

MATHEMATICA

PartitionsP /@ Select[Range[1000], AllTrue[FactorInteger[#][[All, 1]], # <= 3 &] &] (* Jean-François Alcover, Oct 13 2021 *)

PROG

(PARI) \\ here is(n) is test for A003586 inclusion.

is(n)={forprime(p=2, 3, n/=p^valuation(n, p)); n==1}

seq(n)={my(A=List(), i=0); while(#A<n, i++; if(is(i), listput(A, numbpart(i)))); Vec(A)} \\ Andrew Howroyd, Jan 02 2020

CROSSREFS

Cf. A000041, A003586, A090184, A117220, A117222.

Sequence in context: A337347 A087581 A049888 * A073879 A073880 A118332

Adjacent sequences: A117218 A117219 A117220 * A117222 A117223 A117224

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Mar 04 2006

EXTENSIONS

More terms from Michel Marcus, Apr 20 2019

STATUS

approved

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Last modified November 27 05:12 EST 2022. Contains 358362 sequences. (Running on oeis4.)