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

1,2

Comments

Nonprime numbers k such that sigma(k) == 0 (mod tau(k)). - Paolo P. Lava, Jun 11 2013

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)

Links

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

Example

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

Maple

with(numtheory); ListA023883:=proc(q) local n;
for n from 1 to q do if not isprime(n) then  if  sigma(n) mod tau(n)=0 then
print(n); fi; fi; od;  end: ListA023883(10^6); # Paolo P. Lava, Jun 11 2013

Mathematica

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

Crossrefs

Intersection of A003601 and A018252.

Equals A003601 \ A000040.

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

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

Sequence in context: A079010 A324814 A015822 * A230873 A192321 A190272

Adjacent sequences: A023880 A023881 A023882 * A023884 A023885 A023886

Keyword

nonn

Author

Olivier Gérard

Status

approved