A163297 - OEIS

%I #24 Sep 08 2022 08:45:46

%S 1,4,6,9,9,15,11,18,17,22,16,32,18,28,28,35,23,44,25,47,37,41,29,65,

%T 36,47,45,61,35,77,37,68,54,60,54,97,44,66,62,96,48,102,50,90,84,78,

%U 54,130,63,99,78,104,60,126,78,126,86,96,66,174,68,102,110,133,91,151,75,133

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

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

%H G. C. Greubel, <a href="/A163297/b163297.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A000203(n) + A029837(n). - _Michel Marcus_, Jul 14 2015

%p 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

%t Table[DivisorSigma[1,n]+Ceiling[Log[2,n]],{n,70}] (* _Harvey P. Dale_, Nov 21 2014 *)

%o (PARI) vector(60, n, sigma(n)+ceil(log(n)/log(2))) \\ _Michel Marcus_, Jul 14 2015

%o (Magma) [SumOfDivisors(n)+Ceiling(Log(n)/Log(2)) : n in [1..70]]; // _Vincenzo Librandi_, Jul 14 2015

%Y Cf. A000203, A029837.

%K nonn,base,less

%O 1,2

%A _Juri-Stepan Gerasimov_, Jul 25 2009

%E A 37 changed to 36 by _R. J. Mathar_, Jul 26 2009