The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A136404 Square numbers with more divisors than any smaller square number. 5
 1, 4, 16, 36, 144, 576, 900, 3600, 14400, 32400, 44100, 129600, 176400, 705600, 1587600, 2822400, 6350400, 21344400, 57153600, 85377600, 192099600, 341510400, 768398400, 3073593600, 6915585600, 12294374400, 14428814400, 32464832400, 57715257600, 129859329600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Being the square of a number in A002182 is neither necessary nor sufficient. Conjecture: square roots of the terms of this sequence are the same terms as A126098. These are the squares of the indices of the RECORDS of A048691. - R. J. Mathar, Apr 04 2008 The square roots of terms are in A025487. - David A. Corneth, Oct 17 2018 From David A. Corneth, Oct 18 2018: (Start) Records for largest exponents occur at: 1, 2, 5, 15, 25, 35, 200, 203 Least k such that a(k) divides prime(i)^4: 5, 10, 34, 104, 302 Based on these exponents I made the following dataset: primorials <= 10^200 (92 such numbers). 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) LINKS Ray Chandler, Table of n, a(n) for n = 1..582 (first 78 terms from Donovan Johnson, terms to 320 from David A. Corneth) David A. Corneth, Conjectured first 1350 terms EXAMPLE 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. MAPLE 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 with(numtheory): a:=proc(n) if max(seq(tau(j^2), j=1..n-1))

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 15 22:33 EDT 2021. Contains 343937 sequences. (Running on oeis4.)