This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A072980 #18 Apr 22 2025 02:44:40
%S A072980 1,3,11,11,61,11,82,82,82,171,1951,1951,26133,13424,41273,41273,
%T A072980 716656,716656,13871719,13871719,4700888,9548741,222854273,222854273,
%U A072980 222854273,112857219,112857219,112857219,3310041496,20075905417
%N A072980 Numerator of b(n) = Sum_{k'<=n} 1/k', where k' denotes the squarefree numbers.
%C A072980 b(n) was used by Niven in the 70's for an alternative proof of the divergence of the sum of reciprocal of primes.
%H A072980 Ivan Niven, <a href="http://www.jstor.org/stable/2317524">A Proof of the Divergence of sum 1/p</a>, The American Mathematical Monthly, Vol. 78, No. 3 (Mar., 1971), pp. 272-273.
%F A072980 a(n) = A354417(A013928(n+1)). - _Amiram Eldar_, Apr 22 2025
%e A072980 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, ...
%t A072980 Accumulate[Table[If[SquareFreeQ[n], 1, 0]/n, {n, 1, 50}]] // Numerator (* _Amiram Eldar_, Apr 22 2025 *)
%o A072980 (PARI) a(n) = numerator(sum(k=1, n, issquarefree(k)/k)); \\ _Michel Marcus_, Nov 28 2013
%Y A072980 Cf. A005117, A013928, A072983 (denominators), A354417.
%K A072980 easy,frac,nonn
%O A072980 1,2
%A A072980 _Benoit Cloitre_, Aug 21 2002