A329884 Nonunitary superperfect numbers: numbers k such that nusigma(nusigma(k)) = k, where nusigma(k) = sigma(k) - usigma(k) is the sum of nonunitary divisors of k (A048146).

24, 48, 56, 112, 192, 248, 252, 328, 448, 496, 768, 1016, 1792, 1984, 2032, 3240, 6462, 7936, 8128, 11616, 11808, 17412, 20538, 32512, 49152, 65528, 114688, 131056, 507904, 524224, 786432, 1048568, 1835008, 2080768, 2096896, 2097136, 3145728, 4194296, 7340032

Offset: 1

Author

Amiram Eldar, Nov 23 2019

Keywords

• nonn

Comments

Analogous to superperfect numbers (A019279) as nonunitary perfect numbers (A064591) is analogous to perfect numbers (A000396).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..53 (terms below 10^10)

Crossrefs

Cf. A000396, A019279, A034448, A038843, A048146, A064591, A329881.

Programs

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); nusigma[n_] := DivisorSigma[1, n] - usigma[n]; Select[Range[10^6], nusigma[nusigma[#]] == # &]