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Sum of c-divisors of n.
3

%I #24 Dec 26 2013 03:20:16

%S 1,2,4,4,8,9,11,8,14,12,22,17,27,26,26,16,26,24,36,26,39,36,52,33,51,

%T 45,68,48,73,63,57,32,50,44,64,40,67,60,82,50,77,54,96,68,94,88,114,

%U 65,99,87,124,85,124,103,153,92,139,120,170,115,171,140,120,64

%N Sum of c-divisors of n.

%H Peter J. C. Moses, <a href="/A233394/b233394.txt">Table of n, a(n) for n = 1..5000</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%e Let n=23. By the definition of c-divisor (see comment in A124771), 23 has the following c-divisors: 0, 1, 2, 3, 5, 7, 11, 23. So a(23)=52.

%t bitPatt[n_]:=bitPatt[n]=Split[IntegerDigits[n,2],#1>#2||#2==0&];cDivisors[0]:={0};cDivisors[n_]:=Insert[Insert[Map[#[[1]]&,Select[Table[{z,Cases[{bitPatt[n]},Apply[{___,##,___}&,bitPatt[z]]]},{z,n/2}],#[[2]]=!={}&]],0,1],n,-1];Map[Apply[Plus,cDivisors[#]]&,Range[50]] (* _Peter J. C. Moses_, Dec 08 2013 *)

%Y Cf. A114994, A124771.

%K nonn,base

%O 1,2

%A _Vladimir Shevelev_, Dec 08 2013

%E More terms from _Peter J. C. Moses_, Dec 08 2013