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%I #20 Nov 22 2021 10:11:03
%S 1,20,272,65792,2901600,4596800,29016000,4295032832,5789534400,
%T 49085337600,585248256000,960935040000
%N Unitary imperfect numbers: numbers n that equal to their unitary analog of the alternating sum of divisors, A307037(n).
%C 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.
%C a(9) > 5*10^9.
%C Also in the sequence are 49085337600, 585248256000, 960935040000 and 46127952000000.
%C a(13) > 2*10^12. - _Giovanni Resta_, Mar 21 2019
%t f[p_,e_] := p^e + (-1)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^6], a[#] == # &]
%Y Cf. A000215, A127724 (k-imperfect), A127725 (2-imperfect), A127726 (3-imperfect), A307037.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Mar 21 2019
%E a(9)-a(12) from _Giovanni Resta_, Mar 21 2019
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