A335131 a(n) = Sum_{k=1..n} phi(k)*phi(k+1)*phi(k+2), where phi(k) = A000010(k) is Euler's totient function.

2, 6, 22, 38, 86, 134, 278, 374, 614, 774, 1254, 1542, 2118, 2502, 3526, 4294, 6022, 6886, 8614, 9574, 12214, 13974, 17494, 19414, 23734, 26326, 32374, 35062, 41782, 45622, 55222, 60342, 68022, 72630, 82998, 90774, 106326, 113238, 128598, 136278, 156438, 166518

Offset: 1

Author

Vaclav Kotesovec, May 24 2020

Keywords

• nonn

Links

• L. Mirsky, Summation formula involving arithmetic functions, Duke Mathematical Journal, Vol. 16, No. 2 (1949), pp. 261-272.

Crossrefs

Cf. A000010, A002088, A206256, A330319.

Programs

Mathematica

Accumulate[Table[EulerPhi[k]*EulerPhi[k+1]*EulerPhi[k+2], {k, 1, 50}]]

PARI

a(n) = sum(k=1, n, eulerphi(k)*eulerphi(k+1)*eulerphi(k+2)); \\ Michel Marcus, May 24 2020

Formula

a(n) ~ 3*c*n^4 / 8, where c = A206256 = Product_{p prime} (1 - 3/p^2) [Mirsky, 1949, p. 270, formula 30].