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%I #17 Feb 18 2018 11:52:45
%S 1,1,2,4,6,9,12,16,20,25,30,36,42,49,56,64,72,81,90,100,110,121,132,
%T 144,156,169,182,196,210,225,240,256,272,289,306,324,342,361,380,400,
%U 420,441,462,484,506,529,552,576,600,625,650,676,702,729,756,784
%N Smallest number such that the highest common factor of pair of successive terms follows the pattern 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, ..., i.e., b(2n-1) = b(2n) = n given by A004526.
%C (1) a(2n) = n^2, a(2n-1) = n(n+1) = twice the n-th triangular number. (2) Geometric mean of the successive squares interleaved between them.
%C Essentially the same as A002620.
%H G. C. Greubel, <a href="/A076921/b076921.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F Empirical: a(n+1) + a(n) = binomial(n+1,2), a(1) = a(2) = 1. - _G. C. Greubel_, Oct 29 2017
%t Join[{1}, LinearRecurrence[{2, 0, -2, 1}, {1, 2, 4, 6}, 50]] (* _G. C. Greubel_, Oct 29 2017 *)
%Y Cf. A004526.
%K nonn,easy
%O 1,3
%A _Amarnath Murthy_, Oct 17 2002
%E More terms from _Philippe Deléham_, Jun 20 2005
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