A023883 Nonprimes whose average of divisors is an integer.

1, 6, 14, 15, 20, 21, 22, 27, 30, 33, 35, 38, 39, 42, 44, 45, 46, 49, 51, 54, 55, 56, 57, 60, 62, 65, 66, 68, 69, 70, 77, 78, 85, 86, 87, 91, 92, 93, 94, 95, 96, 99, 102, 105, 110, 111, 114, 115, 116, 118, 119, 123, 125, 126, 129, 132, 133, 134, 135, 138

Offset: 1

Author

Olivier Gérard

Keywords

• nonn

Comments

From Bernard Schott, Mar 27 2021: (Start)

Some subsequences of these nonprimes arithmetic numbers.

- Squares of primes of the form 6k+1 (A002476).

- Cubes of odd primes (A030078 \ {8}).

- Semiprimes 2*p where prime p is of the form 4k+3 (A002145).

- Semiprimes 3*p where p prime <> 3 (A001748 \ {9}).

- Integers 4*p where prime p is of the form 6k-1 (A007528). (End)

Examples

			Sigma(22) = 36, tau(22) = 4, sigma(22)/tau(2) = 9, 22 is not prime, hence 22 belongs to this sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (term 1..1000 from Paolo P. Lava)

Crossrefs

Intersection of A003601 and A018252.

Equals A003601 \ A000040.

Cf. A000005 (tau), A000203 (sigma).

Cf. A001748, A002145, A002476, A007528, A030078.

Programs

Mathematica

Select[{Mean[Divisors[#]], #}& /@ Select[Range[140], !PrimeQ[#]&], IntegerQ[#[[1]]]&][[All, 2]] (* Jean-François Alcover, Oct 31 2017 *)