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

1,2

Links

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

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

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 *)

Prog

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

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).

Sequence in context: A227131 A365209 A097863 * A097012 A143348 A000203

Adjacent sequences: A287923 A287924 A287925 * A287927 A287928 A287929

Keyword

nonn,mult

Author

Seiichi Manyama, Jun 15 2017

Extensions

Keyword:mult added by Andrew Howroyd, Jul 20 2018

Status

approved