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

1,2

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A006218, A059246 and also A059248/A035105.

Sequence in context: A135392 A071947 A139343 * A340940 A362464 A384008

Adjacent sequences: A059244 A059245 A059246 * A059248 A059249 A059250

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 21 2001

Status

approved