A074947 Numerators of Sum_{k=1..n} 1/lcm(n,k).

1, 1, 5, 5, 37, 47, 69, 263, 1321, 1429, 9901, 17249, 113741, 161191, 32867, 158363, 3157279, 5777183, 18358381, 20649997, 9258477, 10610101, 24266365, 2411391361, 2299685867, 1072410923, 22804031069, 27841579901, 395718022103

Offset

1,3

Comments

a(n)/A074949(n) is the asymptotic density of numbers that are divisible by their digital root in base n+1 (e.g., A064807 for base 10). - Amiram Eldar, Nov 24 2022

Links

Amiram Eldar, Table of n, a(n) for n = 1..2308

Example

1, 1, 5/6, 5/6, 37/60, 47/60, 69/140, 263/420, 1321/2520, 1429/2520, ...

Mathematica

a[n_] := Numerator @ Sum[1/LCM[k, n], {k, 1, n}]; Array[a, 30] (* Amiram Eldar, Jan 31 2021 *)

Prog

(PARI) a(n)=numerator(sum(i=1, n, 1/lcm(n, i)))

Crossrefs

Cf. A064807, A074949 (denominators).

Sequence in context: A270018 A269876 A139386 * A099757 A271091 A271289

Adjacent sequences: A074944 A074945 A074946 * A074948 A074949 A074950

Keyword

easy,frac,nonn

Author

Benoit Cloitre, Oct 05 2002

Status

approved