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A059246
Numerator of Sum_{j=1..n} d(j)/n, where d = number of divisors function (A000005).
3
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
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
Sequence in context: A349988 A272300 A115406 * A091276 A282574 A076562
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Jan 21 2001
STATUS
approved