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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, 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 Table of n, a(n) for n=1..23. 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}] (* Ryan Propper, Oct 10 2005 *) CROSSREFS Cf. A095209, A095211. Sequence in context: A275801 A158259 A362050 * A156469 A001545 A208954 Adjacent sequences: A095207 A095208 A095209 * A095211 A095212 A095213 KEYWORD nonn AUTHOR Amarnath Murthy, Jun 08 2004 EXTENSIONS More terms from Ryan Propper, Oct 10 2005 a(11) onwards from Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 25 2005 STATUS approved

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Last modified December 10 07:43 EST 2023. Contains 367699 sequences. (Running on oeis4.)