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 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-François 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

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