A100959 Non-semiprimes.

1, 2, 3, 5, 7, 8, 11, 12, 13, 16, 17, 18, 19, 20, 23, 24, 27, 28, 29, 30, 31, 32, 36, 37, 40, 41, 42, 43, 44, 45, 47, 48, 50, 52, 53, 54, 56, 59, 60, 61, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 78, 79, 80, 81, 83, 84, 88, 89, 90, 92, 96, 97, 98, 99, 100, 101, 102, 103, 104

Offset: 1

Author

Reinhard Zumkeller, Nov 24 2004

Keywords

• nonn
• easy

Comments

A001222(a(n)) <> 2; a(n) <> A020639(a(n)) * A006530(a(n)); complement of A001358; A064911(a(n)) = 0.

A174956(a(n)) = 0. - Reinhard Zumkeller, Apr 03 2010

Links

• Donald Alan Morrison, Table of n, a(n) for n = 1..10000
• Donald Alan Morrison, Sage program
• Eric Weisstein's World of Mathematics, Semiprime

Programs

Mathematica

Select[Range[120], ! PrimeOmega[#] == 2 &] (* Vincenzo Librandi, Jun 14 2014 *)

PARI

isok(n) = (bigomega(n) != 2) \\ Michel Marcus, Aug 01 2013

Python

from math import isqrt
from sympy import prime, primepi
def A100959(n):
    def f(x): return n+int(sum(primepi(x//prime(k))-k+1 for k in range(1,primepi(isqrt(x))+1)))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m # Chai Wah Wu, Jul 23 2024

Formula

a(n) = n + O(n log log n/log n). - Charles R Greathouse IV, Dec 29 2024