A333315 a(n) = Sum_{k=1..n} phi(prime(k)-1), where phi is the Euler totient function (A000005).

1, 2, 4, 6, 10, 14, 22, 28, 38, 50, 58, 70, 86, 98, 120, 144, 172, 188, 208, 232, 256, 280, 320, 360, 392, 432, 464, 516, 552, 600, 636, 684, 748, 792, 864, 904, 952, 1006, 1088, 1172, 1260, 1308, 1380, 1444, 1528, 1588, 1636, 1708, 1820, 1892, 2004, 2100, 2164

Offset

1,2

References

József Sándor, Dragoslav S. Mitrinovic, Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 30.

Links

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

S. S. Pillai, On the sum function connected with primitive roots, Proceedings of the Indian Academy of Sciences - Section A, Vol. 13 (1941), pp. 526-529, alternative link.

Eric Weisstein's World of Mathematics, Logarithmic Integral.

Wikipedia, Logarithmic integral function.

Formula

a(n) = Sum_{k=1..n} A008330(k).

a(n) ~ A * Li(n^2), where A is Artin's constant (A005596), and Li(x) is the logarithmic integral function.

Mathematica

Accumulate @ EulerPhi[Select[Range[300], PrimeQ] - 1]

Prog

(PARI) a(n) = sum(k=1, n, eulerphi(prime(k)-1)); \\ Michel Marcus, Mar 15 2020

Crossrefs

Partial sums of A008330.

Cf. A000005, A005596.

Sequence in context: A001747 A048670 A371719 * A307889 A239951 A077625

Adjacent sequences: A333312 A333313 A333314 * A333316 A333317 A333318

Keyword

nonn

Author

Amiram Eldar, Mar 14 2020

Status

approved