

A127725


Numbers n that are 2imperfect.


6




OFFSET

1,1


COMMENTS

This sequence also contains n = 3074457344902430720 = 2^31*5*17*257*65537, which has the product of four Fermat primes (A019434). For this n, 3*n is a 3imperfect number (A127726). [T. D. Noe, Apr 03 2009]
a(9) > 2*10^11.  Donovan Johnson, Feb 07 2013
62549517598720 is also a term (see the "43 terms > 2*10^11" link by Donovan Johnson in A127724).  Michel Marcus, Nov 05 2017


LINKS

Table of n, a(n) for n=1..9.
Laszlo Toth, The alternating sumofdivisors function, 9th Joint Conf. on Math. and Comp. Sci., February 912, 2012, Siofok, Hungary.
Laszlo Toth, A survey of the alternating sumofdivisors function, arXiv:1111.4842 [math.NT], 20112014.


EXAMPLE

40=2^3*5. (84+21)(51) = 20, 2*20 = 40, so 40 is in the sequence.  Jud McCranie, Aug 17 2019


MATHEMATICA

okQ[n_] := 2 Sum[d*(1)^PrimeOmega[n/d], {d, Divisors[n]}] == n;
For[k = 2, k <= 10^9, k = k+2, If[okQ[k], Print[k]]] (* JeanFrançois Alcover, Jan 27 2019 *)


PROG

(PARI) isok(n) = 2*sumdiv(n, d, d*(1)^bigomega(n/d)) == n; \\ Michel Marcus, Oct 28 2017


CROSSREFS

Cf. A127726 (3imperfect numbers), A127724 (kimperfect numbers).
Sequence in context: A003683 A188572 A098519 * A280174 A185619 A048014
Adjacent sequences: A127722 A127723 A127724 * A127726 A127727 A127728


KEYWORD

nonn,more,hard


AUTHOR

T. D. Noe, Jan 25 2007


EXTENSIONS

a(9) by Jud McCranie, Aug 17 2019


STATUS

approved



