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%I #12 Mar 25 2019 04:39:38
%S 4,16,68,256,1028,4112,7200,65536,262148,921600,1036800,1048592,
%T 16777472,88218000,371404800,418535784576
%N Lesser of amicable numbers pair m < n such that A307037(m) = n and A307037(n) = m.
%C The larger counterparts are in A307052.
%C Includes all the pairs of the form {F(k)-1, F(k)} with 0 < k, where F(k) = 2^(2^k) + 1, the k-th Fermat number, is prime.
%C Includes all the pairs of the form {(F(k)-1)*F(m), F(k)*(F(m)-1)} with 0 < k < m, where both F(k) and F(m) are primes.
%C a(17) > 4*10^12. - _Giovanni Resta_, Mar 24 2019
%t f[p_, e_] := p^e + (-1)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; s={}; Do[m = a[n]; If[m > n && a[m] == n, AppendTo[s, n]], {n, 1, 10^7}]; s
%Y Cf. A000215, A307037, A307038, A307052.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Mar 21 2019
%E a(16) from _Giovanni Resta_, Mar 24 2019
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