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

Author

Michel Marcus, Nov 19 2012

Keywords

• nonn

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.

Crossrefs

Cf. A000203, A007955.

Programs

Mathematica

Select[Range[100000], Mod[Times @@ Divisors[DivisorSigma[1, #]], Times @@ Divisors[#]] == 0 &] (* T. D. Noe, Nov 19 2012 *)

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