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
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