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A219362 Numbers n such that the product of divisors of sigma(n) is divisible by the product of divisors of n. 2
1, 6, 24, 28, 120, 224, 270, 496, 672, 864, 3375, 3724, 4320, 4680, 6048, 6200, 6860, 8128, 10976, 11172, 13000, 14336, 15872, 18620, 26208, 27000, 29792, 30240, 32760, 39546, 43008, 43875, 47616, 54880, 55860, 58752, 71680, 80262, 84375, 89376, 98865, 99200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

F. Luca proved that this sequence is infinite.

LINKS

Donovan Johnson, Table of n, a(n) for n = 1..1000

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[100000], Mod[Times @@ Divisors[DivisorSigma[1, #]], Times @@ Divisors[#]] == 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(sigma(n))%A007955(n)==0 \\ Charles R Greathouse IV, Feb 04 2013

CROSSREFS

Cf. A000203, A007955.

Sequence in context: A293453 A118372 A263928 * A226476 A216793 A294900

Adjacent sequences:  A219359 A219360 A219361 * A219363 A219364 A219365

KEYWORD

nonn

AUTHOR

Michel Marcus, Nov 19 2012

STATUS

approved

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Last modified July 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)