A333170 a(n) = Sum_{k=0..n} phi(k^2 + 1), where phi is the Euler totient function (A000010).

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

Amiram Eldar, Table of n, a(n) for n = 0..10000

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.

Cf. A000010, A002522, A335963.

Sequence in context: A079713 A055237 A057434 * A217381 A333997 A162581

Adjacent sequences: A333167 A333168 A333169 * A333171 A333172 A333173

Keyword

nonn

Author

Amiram Eldar, Mar 09 2020

Status

approved