A265391 a(n) = numerator of Sum_{d|n} 1 / tau(d).

1, 3, 3, 11, 3, 9, 3, 25, 11, 9, 3, 11, 3, 9, 9, 137, 3, 11, 3, 11, 9, 9, 3, 25, 11, 9, 25, 11, 3, 27, 3, 49, 9, 9, 9, 121, 3, 9, 9, 25, 3, 27, 3, 11, 11, 9, 3, 137, 11, 11, 9, 11, 3, 25, 9, 25, 9, 9, 3, 33, 3, 9, 11, 363, 9, 27, 3, 11, 9, 27, 3, 275, 3, 9, 11

Offset: 1

Author

Jaroslav Krizek, Dec 08 2015

Keywords

• nonn
• frac

Comments

a(n) = numerator of Sum_{d|n} 1 / A000005(d).

Examples

			For n = 6; divisors d of 6: {1, 2, 3, 6}; tau(d): {1, 2, 2, 4}; Sum_{d|6} 1 / tau(d) = 1/1 + 1/2 + 1/2 + 1/4 = 9 / 4; a(n) = 9 (numerator).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000005, A253139, A265390, A265392 (denominator), A265393.

Programs

Magma

[Numerator(&+[1/NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]

Mathematica

Table[Numerator[Sum[1/DivisorSigma[0, d], {d, Divisors@ n}]], {n, 75}] (* Michael De Vlieger, Dec 09 2015 *)

PARI

a(n) = numerator(sumdiv(n, d, 1/numdiv(d))); \\ Michel Marcus, Dec 09 2015

Formula

a(n) = [Sum_{d|n} 1 / tau(d)] * A265392(n) = A265390(n) * A265392(n) / A253139(n).

a(1) = 1; a(p) = 3 for p = prime.