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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 (list; graph; refs; listen; history; text; internal format)
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. Adams-Watters, 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}] (* Jean-François 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. Adams-Watters, Jun 09 2006

More terms from Jean-François Alcover, Sep 04 2013

STATUS

approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)