A245787 Numbers n such that tau(n)*sigma(n) divides n^2.

1, 26208, 56896, 293760, 997920, 9694080, 23569920, 25159680, 29669760, 67858560, 117849600, 132723360, 208565280, 222963840, 276756480, 427714560, 513786240, 578672640, 628992000, 649503360, 688279680, 714954240, 779950080, 830269440, 979102080, 1037266560

Offset: 1

Author

Jaroslav Krizek, Aug 08 2014

Keywords

• nonn

Comments

a(11) > 10^8. - Derek Orr, Aug 08 2014

Numbers n such that n^2 / (A000005(n) * A000203(n)) is an integer.

Subsequence of A090777 (numbers n such that sigma(n) divides n^2).

Sequence of numbers k(n) = n^2 / (tau(n) * sigma(n)): 1, 104, 889, 612, 945, 7344, …

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..47

Crossrefs

Cf. A000005, A000203, A071707, A090777.

Programs

Magma

[n: n in [1..1000000] | Denominator(n^2 / ((#[d: d in Divisors(n)])* SumOfDivisors(n))) eq 1];

Mathematica

a245787[n_Integer] := Select[Range[n], Divisible[#^2, DivisorSigma[0, #]*DivisorSigma[1, #]]&] (* Michael De Vlieger, Aug 09 2014 *)

PARI

for(n=1,10^8,if(n^2%(numdiv(n)*sigma(n))==0,print1(n,", "))) \\ Derek Orr, Aug 08 2014

Extensions

a(7)-a(10) from Derek Orr, Aug 08 2014

a(11)-a(26) from Jens Kruse Andersen, Aug 13 2014