A216918 Odd numbers with at least 3 distinct prime factors.

105, 165, 195, 231, 255, 273, 285, 315, 345, 357, 385, 399, 429, 435, 455, 465, 483, 495, 525, 555, 561, 585, 595, 609, 615, 627, 645, 651, 663, 665, 693, 705, 715, 735, 741, 759, 765, 777, 795, 805, 819, 825, 855, 861, 885, 897, 903, 915, 935, 945, 957, 969

Offset: 1

Author

Peter Luschny, Oct 02 2012

Keywords

• nonn

Comments

If "at least" is changed to "exactly" we get A278569. - N. J. A. Sloane, Nov 27 2016

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• J. B. Cosgrave, K. Dilcher, Extensions of the Gauss-Wilson Theorem, Integers: Electronic Journal of Combinatorial Number Theory, 8 (2008), p.11.

Crossrefs

A278569 is a subsequence.

Programs

Maple

a:= proc(n) option remember; local k;
      for k from 2+ `if`(n=1, 103, a(n-1)) by 2
        while nops(numtheory[factorset](k))<=2 do od; k
    end:
seq (a(n), n=1..100);  # Alois P. Heinz, Oct 03 2012

Mathematica

Select[Range[1, 999, 2], (PrimeNu[#] >= 3)&] (* Jean-François Alcover, Feb 27 2014 *)

Sage

def is_A216918(n):
    if n % 2 == 0: return False
    return len(n.prime_divisors()) >= 3
def A216918_list(n): return [k for k in srange(1, n + 1, 2) if is_A216918(k)]
A216918_list(969)

Formula

Gauss_factorial(floor(a(n)/2), a(n)) == 1 (mod a(n)). (Cf. A216919)