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Numbers n such that tau(n)*sigma(n) divides n^2.
1

%I #24 Jan 10 2025 12:38:35

%S 1,26208,56896,293760,997920,9694080,23569920,25159680,29669760,

%T 67858560,117849600,132723360,208565280,222963840,276756480,427714560,

%U 513786240,578672640,628992000,649503360,688279680,714954240,779950080,830269440,979102080,1037266560

%N Numbers n such that tau(n)*sigma(n) divides n^2.

%C a(11) > 10^8. - _Derek Orr_, Aug 08 2014

%C Numbers n such that n^2 / (A000005(n) * A000203(n)) is an integer.

%C Subsequence of A090777 (numbers n such that sigma(n) divides n^2).

%C Sequence of numbers k(n) = n^2 / (tau(n) * sigma(n)): 1, 104, 889, 612, 945, 7344, …

%H Jens Kruse Andersen, <a href="/A245787/b245787.txt">Table of n, a(n) for n = 1..47</a>

%t a245787[n_Integer] := Select[Range[n], Divisible[#^2, DivisorSigma[0, #]*DivisorSigma[1, #]]&] (* _Michael De Vlieger_, Aug 09 2014 *)

%o (Magma) [n: n in [1..1000000] | Denominator(n^2 / ((#[d: d in Divisors(n)])* SumOfDivisors(n))) eq 1];

%o (PARI)

%o for(n=1,10^8,if(n^2%(numdiv(n)*sigma(n))==0,print1(n,", "))) \\ _Derek Orr_, Aug 08 2014

%Y Cf. A000005, A000203, A071707, A090777.

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Aug 08 2014

%E a(7)-a(10) from _Derek Orr_, Aug 08 2014

%E a(11)-a(26) from _Jens Kruse Andersen_, Aug 13 2014