A284341 Sum of the divisors of n that are not divisible by 8.

1, 3, 4, 7, 6, 12, 8, 7, 13, 18, 12, 28, 14, 24, 24, 7, 18, 39, 20, 42, 32, 36, 24, 28, 31, 42, 40, 56, 30, 72, 32, 7, 48, 54, 48, 91, 38, 60, 56, 42, 42, 96, 44, 84, 78, 72, 48, 28, 57, 93, 72, 98, 54, 120, 72, 56, 80, 90, 60, 168, 62, 96, 104, 7, 84, 144, 68

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

Cf. Sum of the divisors of n that are not divisible by k: A046913 (k=3), A046897 (k=4), A116073 (k=5), A284326 (k=6), A113957 (k=7), this sequence (k=8), A116607 (k=9), A284344 (k=10).

Sequence in context: A348946 A366744 A073185 * A073183 A353900 A366903

Adjacent sequences: A284338 A284339 A284340 * A284342 A284343 A284344

Keyword

nonn,mult

Author

Seiichi Manyama, Mar 25 2017

Extensions

Keyword:mult added by Andrew Howroyd, Jul 20 2018

Status

approved