OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k>=1} k*x^k/(1 - x^k) - 8*k*x^(8*k)/(1 - x^(8*k)). - Ilya Gutkovskiy, Mar 25 2017
Multiplicative with a(2^e) = 7 if e>=3, and a(p^e) = (p^(e + 1) - 1)/(p - 1) otherwise. - Amiram Eldar, Sep 17 2020
Sum_{k=1..n} a(k) ~ (7*Pi^2/96) * n^2. - Amiram Eldar, Oct 04 2022
MATHEMATICA
Table[Sum[Boole[Mod[d, 8]>0] d , {d, Divisors[n]}], {n, 100}] (* Indranil Ghosh, Mar 25 2017 *)
Table[Total[DeleteCases[Divisors[n], _?(Divisible[#, 8]&)]], {n, 120}] (* Harvey P. Dale, Mar 18 2018 *)
f[p_, e_] := If[p == 2 && e >= 3, 7, (p^(e + 1) - 1)/(p - 1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 17 2020 *)
PROG
(PARI) for(n=1, 100, print1(sumdiv(n, d, ((d%8)>0)*d), ", ")) \\ Indranil Ghosh, Mar 25 2017
(Python)
from sympy import divisors
print([sum([i for i in divisors(n) if i%8]) for n in range(1, 101)]) # Indranil Ghosh, Mar 25 2017
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, Mar 25 2017
EXTENSIONS
Keyword:mult added by Andrew Howroyd, Jul 20 2018
STATUS
approved