A198383 a(n) = Sum_{k=1..n} 2^(n mod k).

1, 2, 4, 5, 10, 10, 20, 22, 37, 40, 80, 72, 144, 158, 278, 283, 566, 548, 1096, 1120, 2106, 2162, 4324, 4210, 8389, 8584, 16650, 16772, 33544, 33194, 66388, 66968, 131882, 132690, 265222, 263607, 527214, 530138, 1052078, 1054254, 2108508, 2103282, 4206564, 4216760

Offset

1,2

Comments

A more precise asymptotic formula is given in the link.

From David Morales Marciel, Oct 19 2015: (Start)

If n is prime then a(n)=2*a(n-1).

It appears that for every (deficient, abundant)-pair of numbers (11+6x, 11+6x+1), a(11+6x) > a(11+6x+1).

(End)

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

B. Cloitre, An asymptotic formula for sum_{k=1..n}x^(n mod k) [broken link, draft]

Formula

a(n) = 2^ceiling(n/2) + O(2^(n/3)).

Mathematica

Table[Sum[2^Mod[n, k], {k, n}], {n, 44}] (* Michael De Vlieger, Oct 19 2015 *)

Prog

(PARI) a(n) = sum(k=1, n, 2^(n%k))

Crossrefs

Cf. A198259.

Sequence in context: A307805 A189767 A173817 * A334268 A220696 A275482

Adjacent sequences: A198380 A198381 A198382 * A198384 A198385 A198386

Keyword

nonn

Author

Benoit Cloitre, Oct 24 2011

Status

approved