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A327633
Noninfinitary perfect numbers: numbers k whose sum of noninfinitary divisors equals k.
5
112, 1344, 32512, 390144, 483840, 5930176, 2952609792
OFFSET
1,1
COMMENTS
Numbers k such that sigma(k) - isigma(k) = A000203(k) - A049417(k) = k.
No more terms below 3 * 10^10.
EXAMPLE
112 is in the sequence since its noninfinitary divisors are {2, 4, 8, 14, 28, 56} whose sum is 112.
MATHEMATICA
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[#] == # &]
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Sep 20 2019
STATUS
approved