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 A055230 Greatest common divisor of largest square dividing n! and squarefree part of n!. 9
 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 3, 3, 6, 10, 10, 10, 5, 5, 1, 21, 42, 42, 7, 7, 14, 42, 6, 6, 5, 5, 10, 330, 165, 231, 231, 231, 462, 2002, 5005, 5005, 4290, 4290, 390, 78, 39, 39, 13, 13, 26, 1326, 102, 102, 17, 935, 13090, 746130, 373065, 373065, 24871, 24871 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..5000 FORMULA a(n) = GCD(A008833(n!), A007913(n!)) = GCD(A008833(A000720(n)), A007913(A000720(n))). EXAMPLE a(5) = 2 because 5! = 120; largest square divisor is 4, squarefree part is 30; GCD(4, 30) = 2. a(7) = 1 because 7! = 5040; the largest square divisor is 144 and the squarefree part is 35 and these are coprime. MATHEMATICA Table[GCD[Times @@ Flatten@ Map[Table[#1, 2 Floor[#2/2]] & @@ # &, #], Times @@ Flatten@ Map[Table[#1, Floor[Mod[#2, 2]]] & @@ # &, #]] &@ FactorInteger[n!], {n, 61}] (* Michael De Vlieger, Jul 26 2016 *) PROG (PARI) a(n) = my(fn=n!, cn=core(fn)); gcd(cn, fn/cn); \\ Michel Marcus, Dec 10 2013 CROSSREFS Cf. A008833, A007913, A000188, A000720. Sequence in context: A293773 A071017 A112049 * A290262 A112050 A283156 Adjacent sequences:  A055227 A055228 A055229 * A055231 A055232 A055233 KEYWORD nonn AUTHOR Labos Elemer, Jun 21 2000 STATUS approved

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Last modified September 23 14:29 EDT 2020. Contains 337310 sequences. (Running on oeis4.)