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A198383 a(n) = Sum_{k=1..n} 2^(n mod k). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 6 23:01 EDT 2020. Contains 335484 sequences. (Running on oeis4.)