A366346 - OEIS

%I #18 Oct 08 2023 08:53:51

%S 0,5,21,40,111,160,270,342,505,812,937,1335,1632,1800,2170,2750,3427,

%T 3672,4415,4967,5260,6152,6800,7847,9305,10102,10490,11360,11782,

%U 12665,16010,17012,18625,19192,22042,22652,24485,26410,27710,29750,31847,32587,36307

%N a(n) = A002070(n) + A036689(n).

%F a(n) = A002070(n) + A036689(n).

%F a(n) = Sum_{y=1..prime(n)} Sum_{x=1..prime(n)} [GCD(f(x,y), prime(n)) = 1],

%F a(n) = Sum_{y=1..prime(n)} Sum_{x=1..prime(n)} (1 - [MOD(f(x,y), prime(n)) = 0]) where f(x,y) = x^3 - x^2 - y^2 - y, in the last two formulas.

%F a(n) = A001248(n) - A272196(n), for n > 1.

%F a(n) = A366362(prime(n), 1).

%t b[n_] := If[n < 1, 0, With[{m = Prime@n}, SeriesCoefficient[q (Product[(1 - q^(11 k)), {k, Ceiling[m/11]}] Product[1 - q^k, {k, m}])^2, {q, 0, m}]]]; Table[Prime[n] (Prime[n] - 1) + b[n], {n, 1, 43}] (* after Michael Somos in A002070, Jul 04 2011 *)

%Y Cf. A366362, A002070, A036689, A001248, A272196.

%K nonn

%O 1,2

%A _Mats Granvik_, Oct 07 2023