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

1,2

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A043373 A054047 A372792 * A285847 A231879 A062973

Adjacent sequences: A056650 A056651 A056652 * A056654 A056655 A056656

Keyword

nonn,easy

Author

Robert G. Wilson v, Aug 30 2000

Extensions

Edited by Vladeta Jovovic, Apr 30 2003

Status

approved