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A003680 Smallest number with 2n divisors.
(Formerly M1586)
20
2, 6, 12, 24, 48, 60, 192, 120, 180, 240, 3072, 360, 12288, 960, 720, 840, 196608, 1260, 786432, 1680, 2880, 15360, 12582912, 2520, 6480, 61440, 6300, 6720, 805306368, 5040, 3221225472, 7560, 46080, 983040, 25920, 10080, 206158430208, 3932160 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Refers to the least number which is multiplicatively n-perfect, i.e. least number m the product of whose divisors equals m^n. - Lekraj Beedassy, Sep 18 2004

For n=1 to 5, a(n) equals second term of A008578, A007422, A162947, A048945, A030628. - Michel Marcus, Feb 04 2014

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 23.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000 (using A005179)

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

FORMULA

Bisection of A005179(n). - Lekraj Beedassy, Sep 21 2004

MATHEMATICA

A005179 = Cases[Import["https://oeis.org/A005179/b005179.txt", "Table"], {_, _}][[All, 2]];

A = {#, DivisorSigma[0, #]}& /@ A005179;

a[n_] := SelectFirst[A, #[[2]] == 2n&][[1]];

a /@ Range[1000] (* Jean-Fran├žois Alcover, Nov 10 2019 *)

PROG

(PARI) a(n)=my(k=2*n); while(numdiv(k)!=2*n, k++); k \\ Charles R Greathouse IV, Jun 23 2017

CROSSREFS

Cf. A061283.

Sequence in context: A305104 A118224 A227068 * A051487 A111286 A058295

Adjacent sequences:  A003677 A003678 A003679 * A003681 A003682 A003683

KEYWORD

nonn,easy,nice,changed

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

More terms from Jud McCranie Oct 15 1997

STATUS

approved

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Last modified November 14 09:51 EST 2019. Contains 329111 sequences. (Running on oeis4.)