A265392 a(n) = denominator of Sum_{d|n} 1 / tau(d).

1, 2, 2, 6, 2, 4, 2, 12, 6, 4, 2, 4, 2, 4, 4, 60, 2, 4, 2, 4, 4, 4, 2, 8, 6, 4, 12, 4, 2, 8, 2, 20, 4, 4, 4, 36, 2, 4, 4, 8, 2, 8, 2, 4, 4, 4, 2, 40, 6, 4, 4, 4, 2, 8, 4, 8, 4, 4, 2, 8, 2, 4, 4, 140, 4, 8, 2, 4, 4, 8, 2, 72, 2, 4, 4, 4, 4, 8, 2, 40, 60, 4, 2

Offset: 1

Author

Jaroslav Krizek, Dec 08 2015

Keywords

• nonn
• frac

Comments

a(n) = denominator 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) = 4 (denominator).
		

Links

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

Crossrefs

Cf. A000005, A253139, A265390, A265391 (numerator), A265392, A265393.

Programs

Magma

[Denominator(&+[1/NumberOfDivisors(d): d in Divisors(n)]): n in [1..1000]]

Mathematica

Table[Denominator[Sum[1/DivisorSigma[0, d], {d, Divisors@ n}]], {n, 83}] (* Michael De Vlieger, Dec 09 2015 *)

PARI

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

Formula

a(n) = A265391(n) / [Sum_{d|n} 1 / tau(d)] = A265391(n) * A253139(n) / A265390(n).

a(1) = 1; a(p) = 2 for p = prime; a(n) = n for numbers 1, 2, 36, 72, ...