A245776 Numerator of (n/tau(n) - sigma(n)/n).

0, -1, 1, -5, 13, -1, 33, 1, 14, 7, 97, -1, 141, 25, 43, 101, 253, 5, 321, 37, 313, 85, 481, 1, 532, 127, 569, 8, 781, 27, 897, 323, 299, 235, 1033, 53, 1293, 301, 1297, 11, 1597, 83, 1761, 179, 173, 457, 2113, 133, 2230, 971, 771, 529, 2701, 163, 2737, 34, 2929, 751, 3361, 11, 3597, 865, 1115

Offset: 1

Author

Jaroslav Krizek, Aug 01 2014

Keywords

• sign
• frac

Comments

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

See A245777 - denominator of (n/tau(n) - sigma(n)/n).

Examples

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

Links

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

Crossrefs

Cf. A000005, A000203, A245777, A245778, A245779, A245782.

Programs

Magma

[Numerator((n/(#[d: d in Divisors(n)]))-(SumOfDivisors(n)/n)): n in [1..1000]]

Mathematica

a245776[n_Integer] :=
Map[Numerator[#/DivisorSigma[0, #] - DivisorSigma[1, #]/#] &,
  Range[n]]; a245776[63] (* Michael De Vlieger, Aug 07 2014 *)

PARI

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

Formula

a(n)/A245777(n) < 1 for numbers n in A245779.

a(n)/A245777(n) is an integer for numbers n in A245778.

a(n) = 1 for n = 3, 8 and 24.

a(n) < 0 for n = 2, 4, 6 and 12.