A059247 Denominator of Sum_{j=1..n} d(j)/n, where d = number of divisors function (A000005).

1, 2, 3, 1, 1, 3, 7, 2, 9, 10, 11, 12, 13, 14, 1, 8, 17, 9, 19, 10, 3, 11, 23, 2, 25, 2, 27, 28, 29, 10, 31, 32, 11, 34, 35, 9, 37, 19, 13, 20, 41, 1, 43, 1, 45, 23, 1, 8, 49, 50, 51, 52, 53, 54, 5, 56, 19, 58, 59, 20, 61, 62, 3, 8, 65, 33, 67, 17, 69, 35, 71

Offset: 1

Author

N. J. A. Sloane, Jan 21 2001

Keywords

• nonn
• frac

Examples

			1, 3/2, 5/3, 2, 2, 7/3, 16/7, 5/2, 23/9, 27/10, ...
		

References

• M. Aigner and G. M. Ziegler, Proofs from The Book, Springer-Verlag, Berlin, 1999; see p. 135.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006218, A059246 and also A059248/A035105.

Programs

Mathematica

Denominator[Table[Sum[DivisorSigma[0, j]/n, {j,1,n}], {n,1,100}]] (* G. C. Greubel, Jan 02 2016 *)

PARI

a(n) = denominator(sum(j=1, n, numdiv(j))/n); \\ Michel Marcus, Jan 03 2017

Python

from math import isqrt, gcd
def A059247(n): return n//gcd(n,(lambda m: 2*sum(n//k for k in range(1, m+1))-m*m)(isqrt(n))) # Chai Wah Wu, Oct 08 2021

Formula

a(n) = denominator(A006218(n)/n). - Michel Marcus, Jan 03 2017