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A147655 Coefficients of x^n in the polynomial given by (1+prime(1)*x)(1+prime(2)*x^2) ... . 13
1, 2, 3, 11, 17, 40, 86, 153, 283, 547, 1069, 1737, 3238, 5340, 9574, 17251, 27897, 45845, 78601, 126725, 207153, 353435, 550422, 881454, 1393870, 2239938, 3473133, 5546789, 8762663, 13341967, 20676253, 31774563, 48248485, 74174759, 111904363, 170184798 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sum of all squarefree numbers whose prime indices sum to n. A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. - Gus Wiseman, May 09 2019

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..9000 (first 1001 terms from Harvey P. Dale)

FORMULA

a(n) = [x^n] Product_{k>=1} 1+prime(k)*x^k. - Alois P. Heinz, Sep 05 2014

EXAMPLE

Form a product from the primes: (1+2x)(1+3x^2)(1+5x^3)...(1+prime(n)x^n)... Multiplying out gives 1+2x+3x^2+11x^3+..., so the sequence begins 1,2,3,11,... .

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      b(n, i-1) +`if`(i>n, 0, b(n-i, i-1)*ithprime(i))))

    end:

a:= n-> b(n$2):

seq(a(n), n=0..50);  # Alois P. Heinz, Sep 05 2014

MATHEMATICA

nn=40; Take[Rest[CoefficientList[Expand[Times@@Table[1+Prime[n]x^n, {n, nn}]], x]], nn] (* Harvey P. Dale, Jul 01 2012 *)

CROSSREFS

Row sums of A246867 and A258323.

Cf. A005117, A015723, A022629, A056239, A066189, A112798, A145519, A147541, A325504, A325506, A325537.

Sequence in context: A023870 A025099 A024597 * A051072 A051096 A051078

Adjacent sequences:  A147652 A147653 A147654 * A147656 A147657 A147658

KEYWORD

nonn

AUTHOR

Neil Fernandez, Nov 09 2008

EXTENSIONS

More terms from Harvey P. Dale, Jul 01 2012

a(0)=1 inserted by Alois P. Heinz, Sep 05 2014

STATUS

approved

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Last modified October 18 00:51 EDT 2019. Contains 328135 sequences. (Running on oeis4.)