A333927 Recursive perfect numbers: numbers k such that A333926(k) = 2*k.

6, 28, 264, 1104, 3360, 75840, 151062912, 606557952, 2171581440

Offset

1,1

Comments

Since a recursive divisor is also a (1+e)-divisor (see A049599), then the first 6 terms and other terms of this sequence coincide with those of A049603.

Links

Table of n, a(n) for n=1..9.

Example

264 is a term since the sum of its recursive divisors is 1 + 2 + 3 + 6 + 8 + 11 + 22 + 24 + 33 + 66 + 88 + 264 = 528 = 2 * 264.

Mathematica

recDivQ[n_, 1] = True; recDivQ[n_, d_] := recDivQ[n, d] = Divisible[n, d] && AllTrue[FactorInteger[d], recDivQ[IntegerExponent[n, First[#]], Last[#]] &]; recDivs[n_] := Select[Divisors[n], recDivQ[n, #] &]; f[p_, e_] := 1 + Total[p^recDivs[e]]; recDivSum[1] = 1; recDivSum[n_] := Times @@ (f @@@ FactorInteger[n]); Select[Range[10^5], recDivSum[#] == 2*# &]

Crossrefs

Cf. A049603, A282446, A333926.

Analogous sequences: A000396, A002827 (unitary), A007357 (infinitary), A054979 (exponential), A064591 (nonunitary).

Sequence in context: A134872 A281003 A049603 * A035527 A220437 A332465

Adjacent sequences: A333924 A333925 A333926 * A333928 A333929 A333930

Keyword

nonn,more

Author

Amiram Eldar, Apr 10 2020

Status

approved