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

Author

Henry Bottomley, Apr 11 2001

Keywords

• nonn
• easy

Comments

Complement of A006093 (primes minus 1).

Numbers which can be written as i*j+i+j, 0A072670(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

Crossrefs

Cf. A060462, A066938, A072672.

Cf. A002808, A006093, A079696.

Programs

Magma

[n-1: n in [2..120] | not IsPrime(n)]; // Vincenzo Librandi, Jun 09 2015

Mathematica

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

PARI

for(n=2,100,if(!isprime(n),print1(n-1,", "))) \\ Derek Orr, Jun 08 2015

Python

from sympy import composite
def A072668(n): return composite(n)-1 # Chai Wah Wu, Aug 02 2024

Formula

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

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

a(n) = A060462(n).