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A127725 Numbers n that are 2-imperfect. 6
2, 12, 40, 252, 880, 10880, 75852, 715816960, 62549517598720 (list; graph; refs; listen; history; text; internal format)
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 3-imperfect 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 sum-of-divisors function, 9th Joint Conf. on Math. and Comp. Sci., February 9-12, 2012, Siofok, Hungary.

Laszlo Toth, A survey of the alternating sum-of-divisors function, arXiv:1111.4842 [math.NT], 2011-2014.

EXAMPLE

40=2^3*5. (8-4+2-1)(5-1) = 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]]] (* Jean-Fran├žois 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 (3-imperfect numbers), A127724 (k-imperfect 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

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Last modified December 5 17:42 EST 2019. Contains 329768 sequences. (Running on oeis4.)