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

Author

Seiichi Manyama, Mar 25 2017

Keywords

• nonn
• mult

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

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).

Programs

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 *)

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

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

Extensions

Keyword:mult added by Andrew Howroyd, Jul 20 2018