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 A147752 Size of the largest subset of {1,2,3,...,n} whose geometric mean is an integer. 3
 1, 1, 1, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n-1) <= a(n) <= max(a(n-1), nu_{A006530(n)}(n!)) where nu_p(n!) is the exponent of the largest power of p that divides n!. - Robert Israel, Jan 02 2018 Let k be the geometric mean of the subset. Then k is in A055932. - David A. Corneth, Jan 03 2018 LINKS David A. Corneth, Possible subsets of {1,2,3,...,n} giving a(n) EXAMPLE For n=4, (1*4)^(1/2)=2 and (1*2*4)^(1/3)=2. No other subset of {1,2,3,4} has integer geometric mean, so a(4)=3. MAPLE ub:= proc(k, n) local p, i, v, t;   p:= max(numtheory:-factorset(k));   t:= 0;   for i from 1 do     v:= floor(n/p^i);     if v = 0 then return t fi;     t:= t+v;   od end proc: f:= proc(n) option remember; local goodk, m, u, s, S;   m:= f(n-1);   u:= ub(n, n);   if u <= m then return m fi;   goodk:= {1} union select(t -> ub(t, n) > m, {\$2..n-1});   S:= combinat:-subsets(goodk);   while not S[finished] do     s:= S[nextvalue]() union {n};     if nops(s) <= m then next fi;     if type(simplify(convert(s, `*`)^(1/nops(s))), integer) then m:= nops(s); if m = u then return m fi fi;   od:   m end proc: f(1):= 1: seq(f(n), n=1..74); # Robert Israel, Jan 02 2018 MATHEMATICA Array[Length@ Last@ Select[Subsets@ Range@ #, IntegerQ@ GeometricMean@ # &] &, 20] (* Michael De Vlieger, Jan 02 2018 *) CROSSREFS Cf. A006530, A147751, A147753. Sequence in context: A227727 A050499 A304431 * A236682 A114227 A187469 Adjacent sequences:  A147749 A147750 A147751 * A147753 A147754 A147755 KEYWORD nonn AUTHOR John W. Layman, Nov 11 2008 EXTENSIONS a(1)-a(3) corrected and a(21)-a(74) from Robert Israel, Jan 02 2018 STATUS approved

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Last modified October 23 09:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)