%I #25 Feb 01 2026 22:53:50

%S 0,1,3,5,7,10,13,16,19,22,26,29,33,37,40,44,49,53,57,61,65,70,74,79,

%T 83,88,92,97,102,107,111,116,121,126,131,136,141,146,151,157,162,167,

%U 172,177,183,188,193,199,204,210,215,221,226,232,237,243,248

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

%H R. J. Mathar, <a href="/A016040/b016040.txt">Table of n, a(n) for n = 1..1000</a>

%H J. W. Sander, <a href="https://www.jstor.org/stable/2974508">A story of binomial coefficients and primes</a>, Amer. Math. Monthly 102 (1995), 802-807.

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

%F a(n) ~ n log n by the prime number theorem. - _Charles R Greathouse IV_, Dec 11 2008

%t Table[Floor[N[Sum[Log[Prime[x]], {x, 1, n}]]], {n, 1, 1000}] (* _Artur Jasinski_, Jan 23 2007 *)

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

%Y Cf. A035158.

%K nonn

%O 1,3

%A _Robert G. Wilson v_

%E New name from _Charles R Greathouse IV_, Dec 11 2008