A072980 - OEIS

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

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OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..30.

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

EXAMPLE

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, ...

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A005117, A013928, A072983 (denominators), A354417.

Sequence in context: A248410 A059200 A232038 * A128500 A365037 A043051

Adjacent sequences: A072977 A072978 A072979 * A072981 A072982 A072983

KEYWORD

easy,frac,nonn

AUTHOR

Benoit Cloitre, Aug 21 2002

STATUS

approved