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A104117 For n=2^k, a(n) = k+1, else 0. 8
1, 2, 0, 3, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums of A103994 (conjectured).

Multiplicative with a(2^e) = 1+e, and a(p^e)=0 for odd primes p and e>=1. Dirichlet convolution square of A209229. - R. J. Mathar, Mar 12 2012

LINKS

Table of n, a(n) for n=1..95.

FORMULA

a(n) = 1 + log_2(n), for n = 1,2,4,8,..; and the rest zeros.

Dirichlet g.f.: 1/(1-2^(-s))^2, i.e., Dirichlet convolution of A036987 (right-shifted, assuming offset 1 there) with itself.

EXAMPLE

a(8) = 4 = sum of row 8 terms of A103994: (1 + 1 + 0 + 1 + 0 + 0 + 0 + 1).

a(8) = 4 = 1 + log_2(8).

PROG

(PARI) a(n)=direuler(p=1, n, if(p==2, 1/(1-X)^2, 1))[n] /* Ralf Stephan, Mar 28 2015 */

(PARI) a(n)=if(n==2^valuation(n, 2), valuation(n, 2)+1, 0) /* Ralf Stephan, Mar 28 2015 */

CROSSREFS

Cf. A103994.

Sequence in context: A138806 A181105 A142971 * A114511 A085199 A338504

Adjacent sequences:  A104114 A104115 A104116 * A104118 A104119 A104120

KEYWORD

nonn,easy,mult

AUTHOR

Gary W. Adamson, Apr 15 2007

EXTENSIONS

More terms and better name from Ralf Stephan, Mar 28 2015

STATUS

approved

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Last modified October 19 09:58 EDT 2021. Contains 348074 sequences. (Running on oeis4.)