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%I #27 Nov 06 2018 11:28:24
%S 1,4,16,36,144,576,900,3600,14400,32400,44100,129600,176400,705600,
%T 1587600,2822400,6350400,21344400,57153600,85377600,192099600,
%U 341510400,768398400,3073593600,6915585600,12294374400,14428814400,32464832400,57715257600,129859329600
%N Square numbers with more divisors than any smaller square number.
%C Being the square of a number in A002182 is neither necessary nor sufficient.
%C Conjecture: square roots of the terms of this sequence are the same terms as A126098.
%C These are the squares of the indices of the RECORDS of A048691. - _R. J. Mathar_, Apr 04 2008
%C The square roots of terms are in A025487. - _David A. Corneth_, Oct 17 2018
%C From _David A. Corneth_, Oct 18 2018: (Start)
%C Records for largest exponents occur at: 1, 2, 5, 15, 25, 35, 200, 203
%C Least k such that a(k) divides prime(i)^4: 5, 10, 34, 104, 302
%C Based on these exponents I made the following dataset:
%C primorials <= 10^200 (92 such numbers).
%C Then made products of primorials <= 10^200 where the exponent of prime(11) is at most 2. Then searched records here. The b-file is checking A025487 squared checked. (End)
%H Ray Chandler, <a href="/A136404/b136404.txt">Table of n, a(n) for n = 1..582</a> (first 78 terms from Donovan Johnson, terms to 320 from David A. Corneth)
%H David A. Corneth, <a href="/A136404/a136404.gp.txt">Conjectured first 1350 terms</a>
%e 900 qualifies because 576 has only 21 divisors and 900 has 27. 1296 does not because 1296 has only 25 divisors as opposed to the 27 of the smaller 900.
%p a := 0 : for n from 1 to 1000000 do ndvs := numtheory[tau](n^2) ; if ndvs > a then printf("%d,",n^2) ; a := ndvs ; fi ; od: # _R. J. Mathar_, Apr 04 2008
%p with(numtheory): a:=proc(n) if max(seq(tau(j^2),j=1..n-1))<tau(n^2) then n^2 else end if end proc: seq(a(n),n=1..10000); # _Emeric Deutsch_, Apr 04 2008
%t With[{s = Array[DivisorSigma[0, #^2] &, 10^6]}, Map[FirstPosition[s, #][[1]]^2 &, Union@ FoldList[Max, s]]] (* _Michael De Vlieger_, Oct 15 2018 *)
%Y Cf. A002182, A025487.
%K nonn
%O 1,2
%A _J. Lowell_, Mar 30 2008
%E More terms from _R. J. Mathar_ and _Donovan Johnson_, Apr 04 2008
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