A327633 Noninfinitary perfect numbers: numbers k whose sum of noninfinitary divisors equals k.

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.

Links

Table of n, a(n) for n=1..7.

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[#] == # &]

Crossrefs

Cf. A000203, A007357, A049417, A064591, A077609, A282900, A282940.

Sequence in context: A188152 A353782 A367363 * A210300 A210293 A203915

Adjacent sequences: A327630 A327631 A327632 * A327634 A327635 A327636

Keyword

nonn,more

Author

Amiram Eldar, Sep 20 2019

Status

approved