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A283529 The number of partitions of n into simple parts. 2
1, 1, 2, 2, 3, 3, 5, 5, 7, 7, 9, 9, 12, 12, 15, 15, 18, 18, 22, 22, 26, 26, 30, 30, 35, 35, 40, 40, 45, 45, 52, 52, 59, 59, 66, 66, 75, 75, 84, 84, 93, 93, 104, 104, 115, 115, 126, 126, 139, 139, 152, 152, 165, 165, 180, 180, 195, 195, 210, 210, 228, 228 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of partitions of n where each part is simple, meaning that each part is in A002110.

LINKS

Giovanni Resta, Table of n, a(n) for n = 0..10000

J. Wang, Reduced phi-partitions of positive integers, Fib. Quart. 31 (4) (1993) 365-369.

FORMULA

G.f.: 1/Product_{i>=0} (1-x^A002110(i)).

EXAMPLE

a(6)=5 counts 1+1+1+1+1+1 = 1+1+1+2 = 1+1+2+2 = 2+2+2 =6.

a(7)=5 counts 1+1+1+1+1+1+1 = 1+1+1+1+1+2 = 1+1+1+2+2 = 1+2+2+2 = 1+6.

MAPLE

isA002110 := proc(n)

    member(n, [1, 2, 6, 30, 210, 2310, 30030, 510510, 9699690, 223092870, 6469693230, 200560490130, 7420738134810, 304250263527210, 13082761331670030, 614889782588491410, 32589158477190044730, 1922760350154212639070]) ;

end proc:

A283529 := proc(n)

    local a, k, issimp, p ;

    a := 0 ;

    for k in combinat[partition](n) do

        issimp := true ;

        for p in k do

            if not isA002110(p) then

                issimp := false;

                break;

            end if;

        end do:

        if issimp then

            a := a+1 ;

        end if;

    end do:

    a ;

end proc:

MATHEMATICA

(* It suffices to compute 3 primorials to get 100 correct terms *)

terms = 100; primorials = FoldList[Times, 1, Prime[Range[3]]]; 1/(Times @@ (1 - x^primorials)) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, May 19 2018 *)

CROSSREFS

Cf. A002110, A064986, A283528.

Sequence in context: A085885 A309685 A309683 * A064986 A349675 A029019

Adjacent sequences:  A283526 A283527 A283528 * A283530 A283531 A283532

KEYWORD

nonn

AUTHOR

R. J. Mathar, Mar 10 2017

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Mar 13 2017

STATUS

approved

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Last modified December 4 05:56 EST 2021. Contains 349470 sequences. (Running on oeis4.)