A287926 Sum of the divisors of n that are not divisible by 49.

1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28, 14, 24, 24, 31, 18, 39, 20, 42, 32, 36, 24, 60, 31, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 91, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 8, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 127, 84, 144

Offset: 1

Author

Seiichi Manyama, Jun 15 2017

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A000203, A213598.

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), A284341 (k=8), A116607 (k=9), A284344 (k=10), A227131 (k=25), this sequence (k=49).

Programs

Mathematica

f[p_, e_] := If[p == 7, 8, (p^(e+1)-1)/(p-1)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Sep 17 2020 *)

PARI

a(n)=sumdiv(n, d, ((d%49)>0)*d); \\ Andrew Howroyd, Jul 20 2018

Formula

Multiplicative with a(7^e) = 8 and a(p^e) = (p^(e+1)-1)/(p-1) otherwise. - Amiram Eldar, Sep 17 2020

Sum_{k=1..n} a(k) ~ (4*Pi^2/49) * n^2. - Amiram Eldar, Oct 04 2022

Extensions

Keyword:mult added by Andrew Howroyd, Jul 20 2018