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

1,1

Links

Table of n, a(n) for n=1..42.

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000010, A002088, A206256, A330319.

Sequence in context: A284632 A350553 A325020 * A147800 A246624 A212872

Adjacent sequences: A335128 A335129 A335130 * A335132 A335133 A335134

Keyword

nonn

Author

Vaclav Kotesovec, May 24 2020

Status

approved