A330319 a(n) = Sum_{i=1..n} phi(i)*phi(i+1), where phi(n) = A000010(n) is Euler's totient function.

1, 3, 7, 15, 23, 35, 59, 83, 107, 147, 187, 235, 307, 355, 419, 547, 643, 751, 895, 991, 1111, 1331, 1507, 1667, 1907, 2123, 2339, 2675, 2899, 3139, 3619, 3939, 4259, 4643, 4931, 5363, 6011, 6443, 6827, 7467, 7947, 8451, 9291, 9771, 10299, 11311, 12047, 12719, 13559, 14199, 14967, 16215, 17151, 17871, 18831

Offset

1,2

References

József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 32.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

A. E. Ingham, Some asymptotic formulae in the theory of numbers, Journal of the London Mathematical Society, Vol. s1-2, No. 3 (1927), pp. 202-208.

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

Formula

a(n) ~ (c/3) * n^3 + O(n^2*log(n)^2), where c = Product_{p prime}(1 - 2/p^2) (A065474). - Amiram Eldar, Mar 05 2020

Mathematica

phi = EulerPhi[Range[56]]; Accumulate[Most[phi] * Rest[phi]] (* Amiram Eldar, Mar 05 2020 *)

Prog

(PARI) a(n) = sum(i=1, n, eulerphi(i)*eulerphi(i+1)); \\ Michel Marcus, Mar 05 2020

Crossrefs

Cf. A000010, A065474, A335131.

Partial sums of A083542.

Sequence in context: A141354 A181106 A131753 * A171503 A326354 A283008

Adjacent sequences: A330316 A330317 A330318 * A330320 A330321 A330322

Keyword

nonn

Author

N. J. A. Sloane, Dec 11 2019

Status

approved