A360524 Numbers k such that A360522(k) = 2*k.

6, 12, 198, 240, 264, 270, 396, 540, 6720, 7920, 11880, 13770, 27540, 221760, 337440, 605880, 2500344, 6072570, 11135520, 12145140, 267193080, 441692160, 1112629770, 2225259540, 14575841280, 48955709880

Offset: 1

Author

Amiram Eldar, Feb 10 2023

Keywords

• nonn
• more

Comments

Analogous to perfect numbers (A000396) with A360522 instead of A000203.

a(27) > 10^11, if it exists.

Examples

			6 is a term since A360522(6) = 12 = 2 * 6.
		

Crossrefs

Cf. A000203, A360522.

Similar sequences: A000396, A002827, A007357, A054979, A322486, A324707.

Programs

Mathematica

f[p_, e_] := p^e + e; q[n_] := Times @@ f @@@ FactorInteger[n] == 2*n; Select[Range[10^6], q]

PARI

is(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^f[i,2] + f[i,2]) == 2*n;}