

A066572


Number of sets of distinct positive integers with geometric mean n.


2



1, 3, 3, 9, 3, 255, 3, 31, 9, 255, 3, 48891, 3, 255, 255, 117, 3, 48891, 3, 48891, 255, 255, 3, 12896331, 9, 255, 31, 48891, 3, 329166915027, 3, 479, 255, 255, 255, 668187863, 3, 255, 255, 12896331, 3, 329166915027, 3, 48891, 48891, 255, 3, 3981060137, 9, 48891, 255, 48891, 3, 12896331, 255, 12896331, 255, 255, 3
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OFFSET

1,2


COMMENTS

a(m) = a(n) if m and n have the same factorization structure.
a(60) is approximately 9.3492e20.  Franklin T. AdamsWatters, Jun 09 2006
Observe that for any prime p, a(p^k) = A066571(k+1) and the largest set is the powers 0..2k of p.


LINKS

Table of n, a(n) for n=1..59.


EXAMPLE

a(2) = 3 as there are three sets viz. {2), {1,4), {1,2,4}, the geometric mean of whose elements is 2.
a(4) = 9: the nine sets are {4}, {1, 16}, {2, 8}, {1, 4, 16}, {2, 4, 8}, {1, 2, 32}, {1, 2, 4, 32}, {1, 2, 8, 16}, {1, 2, 4, 8, 16}.


MATHEMATICA

(* Recomputation using existing values and prime signatures *)
a[1] = 1; a[n_] := Switch[ FactorInteger[n][[All, 2]] // Sort, {1}, 3, {2}, 9, {3}, 31, {4}, 117, {1, 1}, 255, {5}, 479, {1, 2}, 48891, {1, 3}, 12896331, {2, 2}, 668187863, {1, 4}, 3981060137, {1, 1, 1}, 329166915027, _, 0]; Table[ a[n], {n, 1, 59}] (* JeanFrançois Alcover, Sep 04 2013 *)


CROSSREFS

Cf. A066571.
Sequence in context: A157031 A113213 A088032 * A307379 A276147 A300782
Adjacent sequences: A066569 A066570 A066571 * A066573 A066574 A066575


KEYWORD

nonn,nice


AUTHOR

Amarnath Murthy, Dec 19 2001


EXTENSIONS

More terms from Naohiro Nomoto, Dec 26 2001
More terms from Franklin T. AdamsWatters, Jun 09 2006
More terms from JeanFrançois Alcover, Sep 04 2013


STATUS

approved



