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A366346
a(n) = A002070(n) + A036689(n).
1
0, 5, 21, 40, 111, 160, 270, 342, 505, 812, 937, 1335, 1632, 1800, 2170, 2750, 3427, 3672, 4415, 4967, 5260, 6152, 6800, 7847, 9305, 10102, 10490, 11360, 11782, 12665, 16010, 17012, 18625, 19192, 22042, 22652, 24485, 26410, 27710, 29750, 31847, 32587, 36307
OFFSET
1,2
FORMULA
a(n) = A002070(n) + A036689(n).
a(n) = Sum_{y=1..prime(n)} Sum_{x=1..prime(n)} [GCD(f(x,y), prime(n)) = 1],
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.
a(n) = A001248(n) - A272196(n), for n > 1.
a(n) = A366362(prime(n), 1).
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mats Granvik, Oct 07 2023
STATUS
approved