A059246 Numerator of Sum_{j=1..n} d(j)/n, where d = number of divisors function (A000005).

1, 3, 5, 2, 2, 7, 16, 5, 23, 27, 29, 35, 37, 41, 3, 25, 52, 29, 60, 33, 10, 37, 76, 7, 87, 7, 95, 101, 103, 37, 113, 119, 41, 127, 131, 35, 142, 73, 50, 79, 160, 4, 170, 4, 182, 93, 4, 33, 201, 207, 211, 217, 219, 227, 21, 239, 81, 247, 249, 87, 263

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) = numerator(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

Numerator[Table[Sum[DivisorSigma[0, j]/n, {j, 1, n}], {n, 1, 100}]] (* G. C. Greubel, Jan 02 2017 *)

Prog

(PARI) a(n) = numerator(sum(j=1, n, numdiv(j))/n); \\ Michel Marcus, Jan 03 2017
(Python)
from math import gcd, isqrt
def A059246(n): return (m:=-(s:=isqrt(n))**2+(sum(n//k for k in range(1, s+1))<<1))//gcd(n, m) # Chai Wah Wu, Oct 23 2023

Crossrefs

Cf. A006218, A059247.

Sequence in context: A349988 A272300 A115406 * A091276 A282574 A076562

Adjacent sequences: A059243 A059244 A059245 * A059247 A059248 A059249

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 21 2001

Status

approved