A219363 - OEIS

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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, 37200, 86800, 170688, 260400, 334800, 2269200, 2343600, 2864400, 3385200, 4947600, 5291328, 5294800, 10155600, 11048400, 15884400, 18897600, 20422800, 30466800, 33070800, 44094400, 44528400, 61618368, 77338800, 91660800

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OFFSET

1,2

COMMENTS

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

F. Luca proved that this sequence is infinite.

LINKS

Table of n, a(n) for n=1..25.

F. Luca, On the product of divisors of n and sigma(n), J. Inequal. Pure Appl. Math., Volume 4, Issue 2, Article 46, 2003.

MATHEMATICA

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

PROG

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

is(n)=A007955(n)%A007955(sigma(n))==0 \\ Charles R Greathouse IV, Feb 04 2013

CROSSREFS

Cf. A000203, A007955.

Sequence in context: A279862 A112728 A250882 * A254564 A151630 A252166

Adjacent sequences: A219360 A219361 A219362 * A219364 A219365 A219366

KEYWORD

nonn

AUTHOR

Michel Marcus, Nov 19 2012

STATUS

approved