A034713 Dirichlet convolution of powers of 2 (2,4,8,...) with themselves.

4, 16, 32, 80, 128, 320, 512, 1152, 2112, 4352, 8192, 17152, 32768, 66560, 131584, 264448, 524288, 1053696, 2097152, 4203520, 8390656, 16793600, 33554432, 67147776, 134218752, 268500992, 536879104, 1073876992, 2147483648

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Formula

a(n) = 4 * A034733(n).

G.f.: Sum_{k>=1} 2^(k+1)*x^k/(1 - 2*x^k). - Ilya Gutkovskiy, Sep 10 2019

a(n) ~ 2^(n+2). - Vaclav Kotesovec, Sep 11 2019

Mathematica

Table[Sum[2^(d + n/d), {d, Divisors[n]}], {n, 1, 30}] (* Vaclav Kotesovec, Sep 11 2019 *)

Prog

(PARI) a(n) = if(n==0, 1, sumdiv(n, d, 2^d * 2^(n/d) )); \\ Joerg Arndt, Apr 14 2013

Crossrefs

Cf. A000079, A034733.

Sequence in context: A326873 A126032 A296819 * A374001 A101653 A043100

Adjacent sequences: A034710 A034711 A034712 * A034714 A034715 A034716

Keyword

nonn

Author

Erich Friedman

Status

approved