A072668 Numbers one less than composite numbers.

3, 5, 7, 8, 9, 11, 13, 14, 15, 17, 19, 20, 21, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95

Offset

1,1

Comments

Complement of A006093 (primes minus 1).

Numbers which can be written as i*j+i+j, 0<i<=j: A072670(a(n))>0 for n>1.

a(n)! is divisible by a(n)*(a(n)+1)/2, see A060462.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

a(n) = A002808(n) - 1.

a(n) = 2*A002808(n) - A079696(n). - Juri-Stepan Gerasimov, Oct 22 2009

a(n) = A060462(n).

Mathematica

Select[Range[4, 96], CompositeQ] - 1 (* Michael De Vlieger, Dec 10 2020 *)

Prog

(PARI) for(n=2, 100, if(!isprime(n), print1(n-1, ", "))) \\ Derek Orr, Jun 08 2015
(Magma) [n-1: n in [2..120] | not IsPrime(n)]; // Vincenzo Librandi, Jun 09 2015
(Python)
from sympy import composite
def A072668(n): return composite(n)-1 # Chai Wah Wu, Aug 02 2024

Crossrefs

Cf. A060462, A066938, A072672.

Cf. A002808, A006093, A079696.

Sequence in context: A144724 A196990 A060462 * A249433 A300737 A062958

Adjacent sequences: A072665 A072666 A072667 * A072669 A072670 A072671

Keyword

nonn,easy

Author

Henry Bottomley, Apr 11 2001

Status

approved