A072980 Numerator of b(n) = Sum_{k'<=n} 1/k', where k' denotes the squarefree numbers.

1, 3, 11, 11, 61, 11, 82, 82, 82, 171, 1951, 1951, 26133, 13424, 41273, 41273, 716656, 716656, 13871719, 13871719, 4700888, 9548741, 222854273, 222854273, 222854273, 112857219, 112857219, 112857219, 3310041496, 20075905417

Offset: 1

Author

Benoit Cloitre, Aug 21 2002

Keywords

• easy
• frac
• nonn

Comments

b(n) was used by Niven in the 70's for an alternative proof of the divergence of the sum of reciprocal of primes.

Examples

			Fractions begin with 1, 3/2, 11/6, 11/6, 61/30, 11/5, 82/35, 82/35, 82/35, 171/70, 1951/770, 1951/770, ...
		

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, A072983 (denominators), A354417.

Programs

Mathematica

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

PARI

a(n) = numerator(sum(k=1, n, issquarefree(k)/k)); \\ Michel Marcus, Nov 28 2013

Formula

a(n) = A354417(A013928(n+1)). - Amiram Eldar, Apr 22 2025