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

Author

Amiram Eldar, Mar 09 2020

Keywords

• nonn

Examples

			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.
		

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

Crossrefs

Partial sums of A333169.

Cf. A000010, A002522, A335963.

Programs

Mathematica

Accumulate @ Table[EulerPhi[k^2 + 1], {k, 0, 100}]

PARI

a(n) = sum(k=0, n, eulerphi(k^2+1)); \\ Michel Marcus, Mar 10 2020

Formula

a(n) ~ (H/4) * n^3, where H = Product_{p prime, p == 1 (mod 4)} (1 - 2/p^2) = 0.8948412245... (A335963).