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A330319
a(n) = Sum_{i=1..n} phi(i)*phi(i+1), where phi(n) = A000010(n) is Euler's totient function.
4
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
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
Partial sums of A083542.
Sequence in context: A141354 A181106 A131753 * A171503 A326354 A283008
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 11 2019
STATUS
approved