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

1,2

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

Chai Wah Wu, Algorithms for Complementary Sequences, Integers (2025) Vol. 25, Art. No. A95. See p. 24.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A106735 A028743 A082634 * A245303 A359766 A166982

Adjacent sequences: A100956 A100957 A100958 * A100960 A100961 A100962

Keyword

nonn,easy

Author

Reinhard Zumkeller, Nov 24 2004

Status

approved