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

1,2

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

Links

Table of n, a(n) for n=1..12.

Mathematica

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

Crossrefs

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

Sequence in context: A021774 A181384 A269009 * A019613 A021514 A121117

Adjacent sequences: A307035 A307036 A307037 * A307039 A307040 A307041

Keyword

nonn,more

Author

Amiram Eldar, Mar 21 2019

Extensions

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

Status

approved