OFFSET
1,1
COMMENTS
Apart from initial terms, exponents in expansion of A065472 as a product zeta(n)^(-a(n)).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..3000
G. Niklasch, Some number theoretical constants: 1000-digit values [Cached copy]
N. J. A. Sloane, Euler transform
FORMULA
a(n) = 1/n*Sum_{d divides n} (-1)^(d+1)*mobius(n/d)*2^d. - Vladeta Jovovic, Sep 06 2002
G.f.: Sum_{n>=1} moebius(n)*log(1 + 2*x^n)/n, where moebius(n)=A008683(n). - Paul D. Hanna, Oct 13 2010
For n == 0, 1, 3 (mod 4), a(n) = (-1)^(n+1)*A001037(n), which for n>1 also equals (-1)^(n+1)*A059966(n) = (-1)^(n+1)*A060477(n).
For n == 2 (mod 4), a(n) = -(A001037(n) + A001037(n/2)). - George Beck and Max Alekseyev, May 23 2016
a(n) ~ -(-1)^n * 2^n / n. - Vaclav Kotesovec, Jun 12 2018
PROG
(PARI) {a(n)=polcoeff(sum(k=1, n, moebius(k)/k*log(1+2*x^k+x*O(x^n))), n)} \\ Paul D. Hanna, Oct 13 2010
CROSSREFS
KEYWORD
sign
AUTHOR
Christian G. Bower, Jan 04 1999
STATUS
approved