A215260 Nearest integer to log(A002110(n)).

0, 1, 2, 3, 5, 8, 10, 13, 16, 19, 23, 26, 30, 33, 37, 41, 45, 49, 53, 57, 62, 66, 70, 75, 79, 84, 88, 93, 98, 102, 107, 112, 117, 122, 127, 132, 137, 142, 147, 152, 157, 162, 167, 173, 178, 183, 189, 194, 199, 205, 210, 216, 221, 227, 232, 238, 243, 249, 254, 260, 266, 271, 277, 283, 288, 294, 300, 306, 312, 317, 323, 329, 335, 341, 347, 353, 359, 365, 371, 377

Offset: 0

Author

N. J. A. Sloane, Sep 14 2012

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002110, A016040, A057872, A092777, A215259.

Programs

Mathematica

Round@ Log@ FoldList[ Times, 1, Prime@ Range@ 60] (* Robert G. Wilson v, Sep 16 2015 *)

PARI

v=List([t=0]);forprime(p=2,200,t+=log(p);listput(v,round(t))); Vec(v) \\ Charles R Greathouse IV, Sep 23 2012

PARI

a(n) = round(log(factorback(primes(n)))); \\ Michel Marcus, Jan 15 2025

Formula

a(n) ~ n log n, a statement equivalent to the Prime Number Theorem. - Charles R Greathouse IV, Sep 23 2012