A068992 Composite numbers k such that Sum_{d|k} sigma(d)/tau(d) is an integer.

10, 15, 21, 26, 30, 33, 34, 35, 39, 49, 51, 55, 57, 58, 60, 65, 69, 70, 74, 75, 77, 78, 82, 85, 87, 91, 93, 95, 98, 102, 105, 106, 110, 111, 115, 119, 120, 122, 123, 129, 130, 133, 141, 143, 145, 146, 147, 155, 156, 159, 161, 165, 169, 170, 174, 177, 178, 182, 183

Offset: 1

Author

Benoit Cloitre, Apr 06 2002

Keywords

• easy
• nonn

Comments

For p prime, contains p^2 if and only if p == 1 (mod 6). - Robert Israel, May 14 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Contains A024556.

Cf. A000005, A000203.

Programs

Maple

N:= 1000:
V:= Vector(N):
for d from 1 to N do
  r:= numtheory:-sigma(d)/numtheory:-tau(d);
  C:= [seq(i,i=d..N,d)];
  V[C]:= V[C] +~ r
od:
select(t -> not(isprime(t)) and V[t]::integer, [$2..N]); # Robert Israel, May 14 2019

Mathematica

q[n_] := CompositeQ[n] && IntegerQ @ DivisorSum[n, Divide @@ DivisorSigma[{1, 0}, #] &]; Select[Range[200], q] (* Amiram Eldar, Jun 08 2022 *)