A219362 Numbers n such that the product of divisors of sigma(n) is divisible by the product of divisors of n.

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

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: A336550 A118372 A263928 * A226476 A216793 A294900

Adjacent sequences: A219359 A219360 A219361 * A219363 A219364 A219365

Keyword

nonn

Author

Michel Marcus, Nov 19 2012

Status

approved