A083288 Sigma unitary-sigma perfect numbers: numbers m which satisfy the following equation for some integer k: sigma(usigma(m)) = k*m where usigma(m) is sum of unitary divisors of m.

1, 2, 9, 15, 18, 21, 40, 42, 60, 104, 120, 288, 312, 756, 1023, 1170, 2160, 2520, 3024, 4092, 6048, 6552, 8184, 17850, 18720, 29127, 30690, 40768, 58254, 79794, 147312, 285600, 491040, 507780, 556920, 932064, 1276704, 1966020, 3300570, 4134780, 4194288, 4470648

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..71

Example

9 is in the sequence since usigma(9) = 10 and sigma(10) = 18 = 2 * 9 is divisible by 9.

Mathematica

usigma[1]=1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); Select[ Range[10^4], Divisible[DivisorSigma[1, usigma[#]], #] & ] (* Amiram Eldar, Jul 02 2019 *)

Crossrefs

Cf. A000203, A045795, A034448.

Sequence in context: A057481 A359775 A353317 * A272044 A354972 A304803

Adjacent sequences: A083285 A083286 A083287 * A083289 A083290 A083291

Keyword

nonn

Author

Yasutoshi Kohmoto, Jun 05 2003

Extensions

More terms from Amiram Eldar, Jul 02 2019

Status

approved