A307038 Unitary imperfect numbers: numbers n that equal to their unitary analog of the alternating sum of divisors, A307037(n).

1, 20, 272, 65792, 2901600, 4596800, 29016000, 4295032832, 5789534400, 49085337600, 585248256000, 960935040000

Offset: 1

Author

Amiram Eldar, Mar 21 2019

Keywords

• nonn
• more

Comments

Includes all the numbers of the form F(k)*(F(k)-1) with k > 0, where F(k) = 2^(2^k) + 1, the k-th Fermat number, is prime.

a(9) > 5*10^9.

Also in the sequence are 49085337600, 585248256000, 960935040000 and 46127952000000.

a(13) > 2*10^12. - Giovanni Resta, Mar 21 2019

Crossrefs

Cf. A000215, A127724 (k-imperfect), A127725 (2-imperfect), A127726 (3-imperfect), A307037.

Programs

Mathematica

f[p_,e_] := p^e + (-1)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^6], a[#] == # &]

Extensions

a(9)-a(12) from Giovanni Resta, Mar 21 2019