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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 10 12:34 EDT 2020. Contains 335576 sequences. (Running on oeis4.)