A245779 Numbers n such that (n/tau(n) - sigma(n)/n) < 1.

1, 2, 3, 4, 6, 8, 10, 12, 18, 24

Offset: 1

Author

Jaroslav Krizek, Aug 02 2014

Keywords

• nonn
• fini
• full

Comments

Numbers n such that A245776(n)/A245777(n) = n/A000005(n) - A000203(n)/n < 1.

Finite sequence with 10 terms.

Examples

			24 is in sequence because 24/tau(24) - sigma(24)/24 = 24/8 - 60/24 = 1/2.
		

Crossrefs

Cf. A000005, A000203, A245776, A245777, A245778, A245782.

Programs

Magma

[n:n in [1..1000000] | (Numerator((n /(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n))) / (Denominator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n))) lt 1]

Mathematica

a245779[n_Integer] :=
Select[Range[n],
  If[#/DivisorSigma[0, #] - DivisorSigma[1, #]/# < 1, True, False] &]; a245779[1000] (* Michael De Vlieger, Aug 07 2014 *)
Select[Range[25],#/DivisorSigma[0,#]-DivisorSigma[1,#]/#<1&] (* Harvey P. Dale, Nov 21 2023 *)

PARI

for(n=1,10^3, if(n/numdiv(n) - sigma(n)/n < 1, print1(n,", "))) \\ Derek Orr, Aug 02 2014