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%I #32 Oct 04 2022 12:36:21
%S 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,
%T 42,40,56,30,72,32,7,48,54,48,91,38,60,56,42,42,96,44,84,78,72,48,28,
%U 57,93,72,98,54,120,72,56,80,90,60,168,62,96,104,7,84,144,68
%N Sum of the divisors of n that are not divisible by 8.
%H Seiichi Manyama, <a href="/A284341/b284341.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%F 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
%F Sum_{k=1..n} a(k) ~ (7*Pi^2/96) * n^2. - _Amiram Eldar_, Oct 04 2022
%t Table[Sum[Boole[Mod[d,8]>0] d , {d, Divisors[n]}], {n, 100}] (* _Indranil Ghosh_, Mar 25 2017 *)
%t Table[Total[DeleteCases[Divisors[n],_?(Divisible[#,8]&)]],{n,120}] (* _Harvey P. Dale_, Mar 18 2018 *)
%t 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 *)
%o (PARI) for(n=1, 100, print1(sumdiv(n, d, ((d%8)>0)*d),", ")) \\ _Indranil Ghosh_, Mar 25 2017
%o (Python)
%o from sympy import divisors
%o print([sum([i for i in divisors(n) if i%8]) for n in range(1, 101)]) # _Indranil Ghosh_, Mar 25 2017
%Y 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).
%K nonn,mult
%O 1,2
%A _Seiichi Manyama_, Mar 25 2017
%E Keyword:mult added by _Andrew Howroyd_, Jul 20 2018
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