A072983 Denominator of b(n) = Sum_{k'<=n} 1/k', where k' denotes the squarefree numbers.

1, 2, 6, 6, 30, 5, 35, 35, 35, 70, 770, 770, 10010, 5005, 15015, 15015, 255255, 255255, 4849845, 4849845, 1616615, 3233230, 74364290, 74364290, 74364290, 37182145, 37182145, 37182145, 1078282205, 6469693230, 200560490130, 200560490130

Offset

1,2

Comments

b(n) was used by Niven in the 1970's for an alternative proof of the divergence of the sum of reciprocals of the primes.

Links

Table of n, a(n) for n=1..32.

Ivan Niven, A Proof of the Divergence of sum 1/p, The American Mathematical Monthly, Vol. 78, No. 3 (Mar., 1971), pp. 272-273.

Formula

a(n) = A354418(A013928(n+1)). - Amiram Eldar, Apr 22 2025

Mathematica

Accumulate[Table[If[SquareFreeQ[n], 1, 0]/n, {n, 1, 50}]] // Denominator (* Amiram Eldar, Apr 22 2025 *)

Prog

(PARI) a(n)=denominator(sum(k=1, n, issquarefree(k)/k))

Crossrefs

Cf. A005117, A013928, A072980 (numerators), A354418.

Sequence in context: A087310 A130087 A085087 * A379580 A055204 A212397

Adjacent sequences: A072980 A072981 A072982 * A072984 A072985 A072986

Keyword

easy,frac,nonn

Author

Benoit Cloitre, Aug 21 2002

Status

approved