A066572 Number of sets of distinct positive integers with geometric mean n.

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

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

Martin Fuller, Table of n, a(n) for n = 1..359

Martin Fuller, Python program

Example

a(2) = 3 as there are three sets viz. {2}, {1,4}, {1,2,4}, each of which has geometric mean 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: A088032 A348397 A377398 * 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