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%I #5 Apr 10 2020 21:33:18
%S 6,28,264,1104,3360,75840,151062912,606557952,2171581440
%N Recursive perfect numbers: numbers k such that A333926(k) = 2*k.
%C 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.
%e 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.
%t 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*# &]
%Y Cf. A049603, A282446, A333926.
%Y Analogous sequences: A000396, A002827 (unitary), A007357 (infinitary), A054979 (exponential), A064591 (nonunitary).
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Apr 10 2020
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