A016040 - OEIS

A016040

Integer part of Chebyshev's theta function: floor( log(Product_{k=1..n} prime(k)) ).

0, 1, 3, 5, 7, 10, 13, 16, 19, 22, 26, 29, 33, 37, 40, 44, 49, 53, 57, 61, 65, 70, 74, 79, 83, 88, 92, 97, 102, 107, 111, 116, 121, 126, 131, 136, 141, 146, 151, 157, 162, 167, 172, 177, 183, 188, 193, 199, 204, 210, 215, 221, 226, 232, 237, 243, 248

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..1000

J. W. Sander, A story of binomial coefficients and primes, Amer. Math. Monthly 102 (1995), 802-807.

FORMULA

a(n) = A000195(A002110(n)).

a(n) ~ n log n by the prime number theorem. - Charles R Greathouse IV, Dec 11 2008

MATHEMATICA

Table[Floor[N[Sum[Log[Prime[x]], {x, 1, n}]]], {n, 1, 1000}] (* Artur Jasinski, Jan 23 2007 *)

PROG

(PARI) first(nn)= my(t=1); vector(nn, n, log(t*=prime(n))\1); \\ Ruud H.G. van Tol, Jan 29 2026

CROSSREFS

Cf. A035158.

Sequence in context: A079511 A092757 A062430 * A003070 A036604 A001768

Adjacent sequences: A016037 A016038 A016039 * A016041 A016042 A016043

KEYWORD

nonn

AUTHOR

Robert G. Wilson v

EXTENSIONS

New name from Charles R Greathouse IV, Dec 11 2008

STATUS

approved