A064592 Nonunitary doubly perfect numbers: the sum of the nonunitary divisors of n is 2n; i.e., sigma(n) - usigma(n) = 2n.

2520, 31320, 1163160, 2208384, 3053232, 6535296, 13472928, 123165600, 365959296, 4401782352, 5517818880, 612014161920

Offset: 1

Author

Dean Hickerson, Sep 25 2001

Keywords

• nonn
• hard

Comments

There are no others up to 7.9*10^12, but here's a larger one: 2846972800010800140288.

Ligh & Wall found the first 11 terms of this sequence. - Amiram Eldar, Sep 27 2018

Links

• Steve Ligh and Charles R. Wall, Functions of Nonunitary Divisors, Fibonacci Quarterly, Vol. 25 (1987), pp. 333-338.

Crossrefs

Cf. A048146, A064591, A064593, A064594, A064595, A064596.

Programs

Mathematica

nusigma[ n_ ] := DivisorSigma[ 1, n ]-Times@@(1+Power@@#&/@FactorInteger[ n ]); For[ n=1, True, n++, If[ nusigma[ n ]==2n, Print[ n ] ] ]

PARI

isok(n) = sumdiv(n, d, if (gcd(d, n/d)!=1, d)) == 2*n; \\ Michel Marcus, Jul 31 2017