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A030011 Inverse Euler transform of {1, primes}. 5
1, 1, 1, 1, 1, 1, -1, -2, -3, -2, 4, -1, 5, 3, -4, -5, -9, 3, -3, 15, 19, 0, 6, -39, -27, -22, 5, 57, 50, 107, -49, -96, -142, -213, 83, 138, 468, 365, 0, -327, -1215, -618, -526, 957, 2572, 1831, 1673, -2820, -4516, -6155, -3880, 5998, 9282, 18213, 7414 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..5000

N. J. A. Sloane, Transforms

FORMULA

Product_{k>=1} 1/(1-x^k)^{a(k)} = 1 + x + Sum_{n>=1} prime(n) * x^(n + 1).

EXAMPLE

(1-x)^(-1) * (1-x^2)^(-1) * (1-x^3)^(-1) * (1-x^4)^(-1) * (1-x^5)^(-1) * (1-x^6)^(-1) * (1-x^7) * (1-x^8)^2 * ... = 1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 7*x^5 + 11*x^6 + 13*x^7 + 17*x^8 + ... .

CROSSREFS

Cf. A000040, A030010.

Sequence in context: A079528 A143422 A071438 * A286000 A114383 A205689

Adjacent sequences:  A030008 A030009 A030010 * A030012 A030013 A030014

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 17 10:08 EST 2019. Contains 319218 sequences. (Running on oeis4.)