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%I #5 Sep 20 2019 08:58:57
%S 112,1344,32512,390144,483840,5930176,2952609792
%N Noninfinitary perfect numbers: numbers k whose sum of noninfinitary divisors equals k.
%C Numbers k such that sigma(k) - isigma(k) = A000203(k) - A049417(k) = k.
%C No more terms below 3 * 10^10.
%e 112 is in the sequence since its noninfinitary divisors are {2, 4, 8, 14, 28, 56} whose sum is 112.
%t f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], _?(# == 1 &)])); nisigma[1] = 0; nisigma[n_] := DivisorSigma[1, n] - Times @@ (Flatten @ (f @@@ FactorInteger[n]) + 1); Select[Range[500000], nisigma[#] == # &]
%Y Cf. A000203, A007357, A049417, A064591, A077609, A282900, A282940.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Sep 20 2019