cp's OEIS Frontend

A136404 Square numbers with more divisors than any smaller square number.

%I A136404 #27 Nov 06 2018 11:28:24
%S A136404 1,4,16,36,144,576,900,3600,14400,32400,44100,129600,176400,705600,
%T A136404 1587600,2822400,6350400,21344400,57153600,85377600,192099600,
%U A136404 341510400,768398400,3073593600,6915585600,12294374400,14428814400,32464832400,57715257600,129859329600
%N A136404 Square numbers with more divisors than any smaller square number.
%C A136404 Being the square of a number in A002182 is neither necessary nor sufficient.
%C A136404 Conjecture: square roots of the terms of this sequence are the same terms as A126098.
%C A136404 These are the squares of the indices of the RECORDS of A048691. - _R. J. Mathar_, Apr 04 2008
%C A136404 The square roots of terms are in A025487. - _David A. Corneth_, Oct 17 2018
%C A136404 From _David A. Corneth_, Oct 18 2018: (Start)
%C A136404 Records for largest exponents occur at: 1, 2, 5, 15, 25, 35, 200, 203
%C A136404 Least k such that a(k) divides prime(i)^4: 5, 10, 34, 104, 302
%C A136404 Based on these exponents I made the following dataset:
%C A136404 primorials <= 10^200 (92 such numbers).
%C A136404 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 A136404 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 A136404 David A. Corneth, <a href="/A136404/a136404.gp.txt">Conjectured first 1350 terms</a>
%e A136404 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 A136404 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 A136404 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 A136404 With[{s = Array[DivisorSigma[0, #^2] &, 10^6]}, Map[FirstPosition[s, #][[1]]^2 &, Union@ FoldList[Max, s]]] (* _Michael De Vlieger_, Oct 15 2018 *)
%Y A136404 Cf. A002182, A025487.
%K A136404 nonn
%O A136404 1,2
%A A136404 _J. Lowell_, Mar 30 2008
%E A136404 More terms from _R. J. Mathar_ and _Donovan Johnson_, Apr 04 2008