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

Author

Benoit Cloitre, Aug 21 2002

Keywords

• easy
• frac
• nonn

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

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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