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A333170
a(n) = Sum_{k=0..n} phi(k^2 + 1), where phi is the Euler totient function (A000010).
2
1, 2, 6, 10, 26, 38, 74, 94, 142, 182, 282, 342, 454, 518, 714, 826, 1082, 1194, 1434, 1614, 2014, 2206, 2590, 2798, 3374, 3686, 4362, 4650, 5274, 5694, 6526, 6958, 7758, 8190, 9246, 9858, 11154, 11698, 12786, 13546, 15146, 15958, 17366, 18086, 19862, 20874
OFFSET
0,2
REFERENCES
Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 166.
LINKS
FORMULA
a(n) ~ (H/4) * n^3, where H = Product_{p prime, p == 1 (mod 4)} (1 - 2/p^2) = 0.8948412245... (A335963).
EXAMPLE
a(0) = phi(0^2 + 1) = phi(1) = 1.
a(1) = phi(0^2 + 1) + phi(1^2 + 1) = phi(1) + phi(2) = 1 + 1 = 2.
MATHEMATICA
Accumulate @ Table[EulerPhi[k^2 + 1], {k, 0, 100}]
PROG
(PARI) a(n) = sum(k=0, n, eulerphi(k^2+1)); \\ Michel Marcus, Mar 10 2020
CROSSREFS
Partial sums of A333169.
Sequence in context: A079713 A055237 A057434 * A217381 A333997 A162581
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 09 2020
STATUS
approved