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 A061701 Smallest number m such that GCD of d(m^2) and d(m) is 2n+1. 3
 1, 12, 4608, 1728, 1260, 509607936, 2985984, 144, 56358560858112, 5159780352, 302400, 6232805962420322304, 1587600, 900900, 201226394483583074212773888, 15407021574586368, 248832 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Comment from Dean Hickerson, Jun 23, 2001: a(n) exists for every n. In other words, every positive odd integer k is equal to the GCD of d(m^2) and d(m) for some m. To see this, let m = 2^(k^2 - 1) * 3^((k-1)/2). Then d(m) = k^2 * (k+1)/2 and d(m^2) = (2 k^2 - 1) * k. Both of these are divisible by k and (8k-4) d(m) - (2k+1) d(m^2) = k, so the GCD is k. LINKS FORMULA a(n) = Min[m : GCD[d(m^2), d(m)] = 2n+1] EXAMPLE For n = 7, GCD[d(20736),d(144)] = GCD[45,15] = 15 = 2*7+1. CROSSREFS Cf. A000005, A000290, A048691. Sequence in context: A127233 A169657 A009094 * A236067 A134821 A229669 Adjacent sequences:  A061698 A061699 A061700 * A061702 A061703 A061704 KEYWORD nonn AUTHOR Labos Elemer, Jun 18 2001 EXTENSIONS More terms from David Wasserman, Jun 20 2002 STATUS approved

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