A307051 Lesser of amicable numbers pair m < n such that A307037(m) = n and A307037(n) = m.

4, 16, 68, 256, 1028, 4112, 7200, 65536, 262148, 921600, 1036800, 1048592, 16777472, 88218000, 371404800, 418535784576

Offset: 1

Author

Amiram Eldar, Mar 21 2019

Keywords

• nonn
• more

Comments

The larger counterparts are in A307052.

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.

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.

a(17) > 4*10^12. - Giovanni Resta, Mar 24 2019

Crossrefs

Cf. A000215, A307037, A307038, A307052.

Programs

Mathematica

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

Extensions

a(16) from Giovanni Resta, Mar 24 2019