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 A007358 Infinitary multi-perfect numbers. (Formerly M4266) 2
 1, 6, 60, 90, 120, 36720, 73440, 12646368, 22276800, 44553600, 126463680, 133660800, 252927360, 758782080, 4201148160, 8402296320, 28770487200, 287704872000, 575409744000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The sequence contains numbers n such that A049417(n) = k*n for some integer k>=1. A007357 is the subsequence with quotient k=2. Cohen lists n=120, 73440, 44553600, 252927360, 575409744000 as entries with k=3, provides seven entries with k=4 and two entries with k=5. REFERENCES G. L. Cohen, personal communication. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. L. Cohen, On an integer's infinitary divisors, Math. Comp., 54 (1990), 395-411. Michel Marcus, Unexhaustive list of terms PROG (PARI) a049417(n) = {my(b, f=factorint(n)); prod(k=1, #f[, 2], b = binary(f[k, 2]); prod(j=1, #b, if(b[j], 1+f[k, 1]^(2^(#b-j)), 1)))} isok(n) = frac(a049417(n)/n) == 0; \\ Michel Marcus, Sep 05 2018 CROSSREFS Cf. A049417, A007357. Cf. A007691 (analog for sigma). Sequence in context: A168618 A185288 A189000 * A322486 A007357 A002827 Adjacent sequences:  A007355 A007356 A007357 * A007359 A007360 A007361 KEYWORD nonn,more AUTHOR EXTENSIONS a(10)-a(18) from Donovan Johnson, Nov 21 2013 a(1)=1 prepended by Michel Marcus, Sep 04 2018 STATUS approved

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Last modified December 18 23:46 EST 2018. Contains 318245 sequences. (Running on oeis4.)