|
%I #30 Nov 26 2023 03:11:17
%S 1,1,1,1,1,1,1,1,10,1,1,1,1,1,1,1,18,10,1,1,1,1,1,1,26,1,10,1,1,1,1,1,
%T 34,18,1,10,1,1,1,1,42,1,1,1,10,1,1,1,50,26,18,1,1,10,1,1,58,1,1,1,1,
%U 1,10,1,66,34,1,18,1,1,1,10,74,1,26,1,1,1,1,1
%N a(n) = Sum_{d|n, d == 1 (mod 8)} d.
%H Seiichi Manyama, <a href="/A284100/b284100.txt">Table of n, a(n) for n = 1..10000</a>
%F G.f.: Sum_{k>=0} (8*k + 1)*x^(8*k+1)/(1 - x^(8*k+1)). - _Ilya Gutkovskiy_, Mar 21 2017
%F G.f.: Sum_{n >= 1} x^n*(1 + 7*x^(8*n))/(1 - x^(8*n))^2. - _Peter Bala_, Dec 19 2021
%F Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/96 = 0.102808... . - _Amiram Eldar_, Nov 26 2023
%t Table[Sum[If[Mod[d, 8] == 1, d, 0], {d, Divisors[n]}], {n, 80}] (* _Indranil Ghosh_, Mar 21 2017 *)
%t Table[Total[Select[Divisors[n],Mod[#,8]==1&]],{n,80}] (* or *) Table[DivisorSum[n,#&,Mod[#,8]==1&],{n,80}] (* _Harvey P. Dale_, Mar 28 2020 *)
%o (PARI) for(n=1, 80, print1(sumdiv(n, d, if(Mod(d, 8)==1, 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%8==1]) # _Indranil Ghosh_, Mar 21 2017
%Y Cf. A277090.
%Y Cf. Sum_{d|n, d==1 (mod k)} d: A000593 (k=2), A078181 (k=3), A050449 (k=4), A284097 (k=5), A284098 (k=6), A284099 (k=7), this sequence (k=8).
%K nonn,easy
%O 1,9
%A _Seiichi Manyama_, Mar 20 2017
|
