%I #119 Jun 25 2023 10:39:44

%S 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,

%T 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,

%U 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

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

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

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

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

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

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

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

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

%Y Cf. A279061, A363808.

%K nonn

%O 1,7

%A _Seiichi Manyama_, Jun 24 2023