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 A095210 a(n) = least multiple of n such that the geometric mean of a(1), ..., a(n) is an integer. 3
 1, 4, 54, 96, 37500, 60, 49412580, 107520, 16533720, 2520, 718985409939720, 27720, 8395697954737253160, 360360, 360360, 23616552960, 596208601546720632677647440, 12252240, 24240072441867520569208380462960, 232792560, 232792560, 232792560, 4860817599682675053132316060135142981520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(11), if it exists, is greater than 10^12. - Ryan Propper (rpropper(AT)stanford.edu), Oct 10 2005 Comments from Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 25 2005: "Sequence is infinite. For a prime p, a(p) has p^p as a factor. Factoring the a(n) gives the pattern for the exponents: [2, 1] [2, 2] [2, 1; 3, 3] [2, 5; 3, 1] [2, 2; 3, 1; 5, 5] [2, 2; 3, 1; 5, 1] [2, 2; 3, 1; 5, 1; 7, 7] [2, 10; 3, 1; 5, 1; 7, 1] [2, 3; 3, 10; 5, 1; 7, 1] [2, 3; 3, 2; 5, 1; 7, 1] [2, 3; 3, 2; 5, 1; 7, 1; 11, 11] [2, 3; 3, 2; 5, 1; 7, 1; 11, 1] [2, 3; 3, 2; 5, 1; 7, 1; 11, 1; 13, 13] [2, 3; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1] [2, 3; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1] [2, 19; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1] [2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 17] [2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1] [2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 19] [2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 1] [2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 1] [2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 1] [2, 4; 3, 2; 5, 1; 7, 1; 11, 1; 13, 1; 17, 1; 19, 1; 23, 23]." LINKS EXAMPLE (1*4*54*96)^(1/4)= (20736)^(1/4) = 12. a(5)=37500=2^2*3*5^5 a(11)=718985409939720=2^3*3^2*5*7*11^11 MATHEMATICA p = 1; Do[k = 1; While[ !IntegerQ[(p*k*n)^(1/n)], k++ ]; Print[k*n]; p *= (k*n), {n, 1, 10}] (Propper) CROSSREFS Cf. A095209, A095211. Sequence in context: A099340 A221605 A158259 * A156469 A001545 A208954 Adjacent sequences:  A095207 A095208 A095209 * A095211 A095212 A095213 KEYWORD nonn AUTHOR Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 08 2004 EXTENSIONS More terms from Ryan Propper (rpropper(AT)stanford.edu), Oct 10 2005 a(11) onwards from Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 25 2005 STATUS approved

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