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Search: id:A136404
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| A136404 |
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Square numbers with more divisors than any smaller square number. |
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+0
1
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| 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, 519437318400, 1168733966400, 2077749273600
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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 (mathar(AT)strw.leidenuniv.nl), Apr 04 2008
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EXAMPLE
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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.
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), Apr 04 2008
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 (deutsch(AT)duke.poly.edu), Apr 04 2008
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CROSSREFS
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Cf. A002182.
Adjacent sequences: A136401 A136402 A136403 this_sequence A136405 A136406 A136407
Sequence in context: A005722 A075408 A114268 this_sequence A046952 A081456 A130279
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KEYWORD
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nonn
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AUTHOR
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J. Lowell (jhbubby(AT)mindspring.com), Mar 30 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Donovan Johnson (donovan.johnson(AT)yahoo.com), Apr 04 2008
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