login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A127726 Numbers n that are 3-imperfect. 6
6, 120, 126, 2520, 2640, 30240, 32640, 37800, 37926, 55440, 685440, 758520, 831600, 2600640, 5533920, 6917400, 9102240, 10281600, 11377800, 16687440, 152182800, 206317440, 250311600, 475917120, 866829600, 1665709920, 1881532800, 2082137400, 2147450880 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The new terms come from the paper by Zhou and Zhu. This sequence also contains n = 9223372034707292160 = 2^31*3*5*17*257*65537, which has the product of five Fermat primes (A019434). For this n, n/3 is a 2-imperfect number (A127725). [T. D. Noe, Apr 03 2009]

LINKS

Michel Marcus, Table of n, a(n) for n = 1..75 (terms < 10^20) (terms 1 to 35 from Donovan Johnson)

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

Weiyi Zhou and Long Zhu, On k-imperfect numbers, INTEGERS: Electronic Journal of Combinatorial Number Theory, 9 (2009), #A01.

Michel Marcus, More 3-imperfect numbers

MATHEMATICA

okQ[n_] := 3 Sum[d*(-1)^PrimeOmega[n/d], {d, Divisors[n]}] == n;

For[k = 3, k < 10^6, k = k + 3, If[okQ[k], Print[k]]] (* Jean-Fran├žois Alcover, Feb 01 2019 *)

PROG

(PARI) isok(n) = 3*sumdiv(n, d, d*(-1)^bigomega(n/d)) == n; \\ Michel Marcus, Oct 28 2017

CROSSREFS

Cf. A127724 (k-imperfect), A127725 (2-imperfect).

Sequence in context: A271648 A290341 A246827 * A117063 A178911 A227027

Adjacent sequences:  A127723 A127724 A127725 * A127727 A127728 A127729

KEYWORD

nonn

AUTHOR

T. D. Noe, Jan 25 2007

EXTENSIONS

Extended by T. D. Noe, Apr 03 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 22:27 EST 2019. Contains 329880 sequences. (Running on oeis4.)