A056653 Composite numbers together with 1 but excluding 4.

1, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95

Offset: 1

Author

Robert G. Wilson v, Aug 30 2000

Keywords

• nonn
• easy

Comments

These are also the numbers k such that k divides (k-1)!.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A018252, A002808, A226198, A014076 (odd terms).

Programs

Maple

for n from 1 to 100 do
  if irem(factorial(n-1),n) = 0 then print(n) end if;
end do: # Peter Bala, Jan 24 2017

Mathematica

Select[ Range[ 1, 100 ], Mod[ (# - 1)!, # ] == 0 & ]
Join[{1},Select[Range[5,100],CompositeQ]] (* Harvey P. Dale, Jun 14 2024 *)

Python

from sympy import composite
def A056653(n): return composite(n) if n>1 else 1 # Chai Wah Wu, Jul 31 2024

Extensions

Edited by Vladeta Jovovic, Apr 30 2003