A245777 Denominator of (n / tau(n) - sigma(n) / n).

1, 2, 6, 12, 10, 2, 14, 8, 9, 10, 22, 3, 26, 14, 20, 80, 34, 6, 38, 30, 84, 22, 46, 2, 75, 26, 108, 3, 58, 20, 62, 96, 44, 34, 140, 36, 74, 38, 156, 4, 82, 28, 86, 33, 30, 46, 94, 60, 147, 150, 68, 78, 106, 36, 220, 7, 228, 58, 118, 5, 122, 62, 126, 448, 260

Offset: 1

Author

Jaroslav Krizek, Aug 01 2014

Keywords

• nonn
• frac

Comments

Denominator of (n / A000005(n) - A000203(n) / n).

See A245776 - numerator of (n / tau(n) - sigma(n) / n).

If n is an odd prime, a(n) = 2*n. - Robert Israel, Aug 01 2014

First deviation from A245785 (denominator of (n/tau(n) + sigma(n)/n)) is at a(300); a(300) = 75, A245785(300) = 25. Sequence of numbers n such that A245785(n) is not equal to a(n): 300, 768, 1452, 1764, 2100, 3468, 3900, 5376, 5700, 6084, 6348, 9075, 9300, ... See (Magma) [n: n in [1..10000] | (Denominator((n/(#[d: d in Divisors(n)]))+(SumOfDivisors(n)/n))) - (Denominator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n))) ne 0] - Jaroslav Krizek, Aug 15 2014

Examples

			For n = 9; a(9) = denominator(9/tau(9) - sigma(9)/9) = denominator(9/3 - 13/9) = denominator(14/9) = 9.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000203, A245776, A245778, A245779, A245782.

Programs

Magma

[Denominator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n)): n in [1..100]]

Mathematica

Table[Denominator[n/DivisorSigma[0, n] - DivisorSigma[1, n]/n], {n, 70}] (* Alonso del Arte, Aug 15 2014 *)

PARI

vector(150, n, denominator(n/numdiv(n) - sigma(n)/n)) \\ Derek Orr, Aug 01 2014

Formula

A245776(n) / a(n) < 1 for numbers n in A245779.

A245776(n) / a(n) = integer for numbers n in A245778.

a(n) = 1 for numbers n in A245778.