A174478 a(n) = Sum_{d|n} d*2^(n/d)*tau(d).

2, 12, 20, 56, 52, 168, 156, 432, 614, 1272, 2092, 4784, 8244, 17064, 33160, 67040, 131140, 265092, 524364, 1053616, 2098200, 4202760, 8388700, 16797216, 33554902, 67141944, 134221232, 268503312, 536871028, 1073881488, 2147483772

Offset

1,1

Comments

tau(n) = A000005(n) = the number of divisors of n.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Logarithmic derivative of A174477.

Mathematica

Table[With[{d=Divisors[n]}, Total[d 2^(n/d) DivisorSigma[0, d]]], {n, 40}] (* Harvey P. Dale, Nov 13 2021 *)

Prog

(PARI) {a(n)=sumdiv(n, d, d*2^(n/d)*sigma(d, 0))}

Crossrefs

Cf. A174477, A000005 (tau).

Sequence in context: A145622 A266050 A291698 * A331947 A349469 A145634

Adjacent sequences: A174475 A174476 A174477 * A174479 A174480 A174481

Keyword

nonn

Author

Paul D. Hanna, Apr 04 2010

Status

approved