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

1,1

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.

Formula

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

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 *)

Prog

(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)

Crossrefs

A278569 is a subsequence.

Sequence in context: A252069 A133509 A013590 * A278569 A046389 A154430

Adjacent sequences: A216915 A216916 A216917 * A216919 A216920 A216921

Keyword

nonn

Author

Peter Luschny, Oct 02 2012

Status

approved