A361691 Number of divisors of 7*n-1 of form 7*k+1.

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 1, 3, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 3, 2, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1

Offset

1,7

Comments

Also number of divisors of 7*n-1 of form 7*k+6.

Links

Table of n, a(n) for n=1..100.

Formula

a(n) = A279061(7*n-1) = A363808(7*n-1).

G.f.: Sum_{k>0} x^(6*k-5)/(1 - x^(7*k-6)).

G.f.: Sum_{k>0} x^k/(1 - x^(7*k-1)).

Mathematica

a[n_] := DivisorSum[7*n - 1, 1 &, Mod[#, 7] == 1 &]; Array[a, 100] (* Amiram Eldar, Jun 25 2023 *)

Prog

(PARI) a(n) = sumdiv(7*n-1, d, d%7==1);

Crossrefs

Cf. A363854, A363855, A363856, A363857, A363858.

Cf. A279061, A363808.

Sequence in context: A309004 A355382 A304779 * A334933 A371451 A049100

Adjacent sequences: A361688 A361689 A361690 * A361692 A361693 A361694

Keyword

nonn

Author

Seiichi Manyama, Jun 24 2023

Status

approved