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Number of divisors of 7*n-6 of form 7*k+2.
0

%I #11 Jun 25 2023 10:40:21

%S 0,1,0,1,0,2,0,1,0,2,0,1,0,2,1,1,0,2,0,1,0,2,0,2,0,3,0,1,0,2,0,1,1,2,

%T 0,1,1,2,0,1,0,4,0,1,0,2,0,2,0,2,1,1,0,2,0,1,0,3,1,3,0,2,0,1,0,2,0,1,

%U 1,3,0,1,0,3,0,1,0,4,0,1,1,2,1,1,0,2,1,1,0,3,0,2,0,2,0,3,0,2,0,1

%N Number of divisors of 7*n-6 of form 7*k+2.

%C Also number of divisors of 7*n-6 of form 7*k+4.

%F a(n) = A363795(7*n-6) = A363806(7*n-6).

%F G.f.: Sum_{k>0} x^(4*k-2)/(1 - x^(7*k-5)).

%F G.f.: Sum_{k>0} x^(2*k)/(1 - x^(7*k-3)).

%t a[n_] := DivisorSum[7*n - 6, 1 &, Mod[#, 7] == 2 &]; Array[a, 100] (* _Amiram Eldar_, Jun 25 2023 *)

%o (PARI) a(n) = sumdiv(7*n-6, d, d%7==2);

%Y Cf. A363795, A363806.

%K nonn

%O 1,6

%A _Seiichi Manyama_, Jun 25 2023