

A127726


Numbers n that are 3imperfect.


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 2imperfect 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 sumofdivisors function, arXiv:1111.4842 [math.NT], 20112014.
Weiyi Zhou and Long Zhu, On kimperfect numbers, INTEGERS: Electronic Journal of Combinatorial Number Theory, 9 (2009), #A01.
Michel Marcus, More 3imperfect 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]]] (* JeanFrançois 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 (kimperfect), A127725 (2imperfect).
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



