A163297 a(n) = sum of divisors of n plus length of the binary expansion of n.

1, 4, 6, 9, 9, 15, 11, 18, 17, 22, 16, 32, 18, 28, 28, 35, 23, 44, 25, 47, 37, 41, 29, 65, 36, 47, 45, 61, 35, 77, 37, 68, 54, 60, 54, 97, 44, 66, 62, 96, 48, 102, 50, 90, 84, 78, 54, 130, 63, 99, 78, 104, 60, 126, 78, 126, 86, 96, 66, 174, 68, 102, 110, 133, 91, 151, 75, 133

Offset

1,2

Comments

The length of the binary expansion of n is ceiling(log_2(n)).

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = A000203(n) + A029837(n). - Michel Marcus, Jul 14 2015

Maple

A029837 := proc(n) ceil(log[2](n)) ; end: A163297 := proc(n) numtheory[sigma](n)+A029837(n) ; end: seq(A163297(n), n=1..100) ; # R. J. Mathar, Jul 26 2009

Mathematica

Table[DivisorSigma[1, n]+Ceiling[Log[2, n]], {n, 70}] (* Harvey P. Dale, Nov 21 2014 *)

Prog

(PARI) vector(60, n, sigma(n)+ceil(log(n)/log(2))) \\ Michel Marcus, Jul 14 2015
(Magma) [SumOfDivisors(n)+Ceiling(Log(n)/Log(2)) : n in [1..70]]; // Vincenzo Librandi, Jul 14 2015

Crossrefs

Cf. A000203, A029837.

Sequence in context: A341577 A094115 A339856 * A051679 A010378 A166593

Adjacent sequences: A163294 A163295 A163296 * A163298 A163299 A163300

Keyword

nonn,base,less

Author

Juri-Stepan Gerasimov, Jul 25 2009

Extensions

A 37 changed to 36 by R. J. Mathar, Jul 26 2009

Status

approved