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 A219363 Numbers such that the product of divisors of n is divisible by the product of divisors of sigma(n). 1

%I

%S 1,37200,86800,170688,260400,334800,2269200,2343600,2864400,3385200,

%T 4947600,5291328,5294800,10155600,11048400,15884400,18897600,20422800,

%U 30466800,33070800,44094400,44528400,61618368,77338800,91660800

%N Numbers such that the product of divisors of n is divisible by the product of divisors of sigma(n).

%C That is, numbers such that A007955(A000203(n)) | A007955(n).

%C F. Luca proved that this sequence is infinite.

%H F. Luca, <a href="http://jipam.vu.edu.au/v4n2/021_03.html">On the product of divisors of n and sigma(n)</a>, J. Inequal. Pure Appl. Math., Volume 4, Issue 2, Article 46, 2003.

%t Select[Range[1000000], Mod[Times @@ Divisors[#], Times @@ Divisors[DivisorSigma[1, #]]] == 0 &] (* _T. D. Noe_, Nov 19 2012 *)

%o (PARI) A007955(n)=if(issquare(n, &n), n^numdiv(n^2), n^(numdiv(n)/2))

%o is(n)=A007955(n)%A007955(sigma(n))==0 \\ _Charles R Greathouse IV_, Feb 04 2013

%Y Cf. A000203, A007955.

%K nonn

%O 1,2

%A _Michel Marcus_, Nov 19 2012

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Last modified August 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)