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Sum_{d|n, d=1 or 6 mod 7} d.
3

%I #15 Mar 24 2017 10:20:56

%S 1,1,1,1,1,7,1,9,1,1,1,7,14,1,16,9,1,7,1,21,1,23,1,15,1,14,28,1,30,22,

%T 1,9,1,35,1,43,1,1,14,29,42,7,44,23,16,1,1,63,1,51,1,14,1,34,56,9,58,

%U 30,1,42,1,63,1,73,14,29,1,35,70,1,72,51,1,1,16,77,1

%N Sum_{d|n, d=1 or 6 mod 7} d.

%H Seiichi Manyama, <a href="/A284151/b284151.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A284099(n) + A284105(n). - _R. J. Mathar_, Mar 21 2017

%t Table[Sum[If[Mod[d, 7] == 1 || Mod[d, 7]==6, d, 0], {d, Divisors[n]}], {n, 80}] (* _Indranil Ghosh_, Mar 21 2017 *)

%o (PARI) for(n=1, 80, print1(sumdiv(n, d, if(d%7==1 || d%7==6, d, 0)), ", ")) \\ _Indranil Ghosh_, Mar 21 2017

%o (Python)

%o from sympy import divisors

%o def a(n): return sum([d for d in divisors(n) if d%7==1 or d%7 == 6]) # _Indranil Ghosh_, Mar 21 2017

%Y Cf. A035430, A284099, A284105.

%Y Cf. Sum_{d|n, d=1 or k-1 mod k} d: A046913 (k=3), A000593 (k=4), A284150 (k=5), A186099 (k=6), this sequence (k=7).

%K nonn

%O 1,6

%A _Seiichi Manyama_, Mar 21 2017