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Number of divisors of 7*n-4 of form 7*k+6.
5

%I #15 Jun 25 2023 09:40:32

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

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

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

%N Number of divisors of 7*n-4 of form 7*k+6.

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

%F a(n) = A363806(7*n-4) = A363808(7*n-4).

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

%F G.f.: Sum_{k>0} x^(6*k-2)/(1 - x^(7*k-3)).

%t a[n_] := DivisorSum[7*n - 4, 1 &, Mod[#, 7] == 6 &]; Array[a, 100] (* _Amiram Eldar_, Jun 25 2023 *)

%o (PARI) a(n) = sumdiv(7*n-4, d, d%7==6);

%Y Cf. A361691, A363854, A363855, A363857, A363858.

%Y Cf. A363806, A363808.

%K nonn

%O 1,16

%A _Seiichi Manyama_, Jun 24 2023