Search: id:A061701
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%I A061701
%S A061701 1,12,4608,1728,1260,509607936,2985984,144,56358560858112,5159780352,
%T A061701 302400,6232805962420322304,1587600,900900,201226394483583074212773888,
%U A061701 15407021574586368,248832
%N A061701 Smallest number m such that GCD of d(m^2) and d(m) is 2n+1.
%C A061701 Comment from Dean Hickerson (dean.hickerson(AT)yahoo.com), 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.
%F A061701 a(n) = Min[m : GCD[d(m^2), d(m)] = 2n+1]
%e A061701 For n = 7, GCD[d(20736),d(144)] = GCD[45,15] = 15 = 2*7+1.
%Y A061701 Cf. A000005, A000290, A048691.
%Y A061701 Sequence in context: A096732 A127233 A009094 this_sequence A134821 A013508 
               A003793
%Y A061701 Adjacent sequences: A061698 A061699 A061700 this_sequence A061702 A061703 
               A061704
%K A061701 nonn
%O A061701 0,2
%A A061701 Labos E. (labos(AT)ana.sote.hu), Jun 18 2001
%E A061701 More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jun 20 
               2002

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