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A284341 Sum of the divisors of n that are not divisible by 8. 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 (list; graph; refs; listen; history; text; internal format)
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

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>0]) 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: A292288 A113957 A073185 * A073183 A049418 A333926

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

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Last modified March 2 11:24 EST 2021. Contains 341746 sequences. (Running on oeis4.)