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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
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 (list; graph; refs; listen; history; text; internal format)
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: A062085 A284632 A325020 * A147800 A246624 A212872

Adjacent sequences:  A335127 A335128 A335129 * A335132 A335133 A335134

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, May 24 2020

STATUS

approved

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Last modified July 8 17:40 EDT 2020. Contains 335524 sequences. (Running on oeis4.)