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 A101992 #18 Feb 16 2025 08:32:55
%S A101992 1,1,11,49,59,131,559,14533,15289,33031,34417,441877,452173,2224829,
%T A101992 9034451,152504587,155227307,2932982513,2967901397,2945730677,
%U A101992 2971126229,6189267977,6250111487,155668689479,156604743479,1404034379311,1411857116311,5835711932717
%N A101992 Numerator of Sum_{i=2..n} (-1)^i/(i*phi(i)).
%C A101992 I conjecture that there exists a limit for Sum_{i>=2} (-1)^i/(i*phi(i)) which is ca. 0.558.
%H A101992 Amiram Eldar, <a href="/A101992/b101992.txt">Table of n, a(n) for n = 2..2296</a>
%H A101992 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%F A101992 a(n) = numerator( Sum_{i=2..n} (-1)^i/(i*phi(i)) ).
%F A101992 Sum_{i>=2} (-1)^i/(i*phi(i)) = 1 - (1/5) * A065484 = 0.5592286807... . - _Amiram Eldar_, Nov 21 2022
%e A101992 a(4) = 11 because Sum_{i=2..4} (-1)^i/(i*phi(i)) = 1/2 - 1/6 + 1/8 = 11/24, and the numerator of 11/24 is 11.
%t A101992 (* Generating the sum : *) f[n_Integer]/; n >= 2 := Sum[(-1)^i/(i*EulerPhi[i]), {i, 2, n}]; (* Getting the numerator: *) a[n_Integer]/; n >=2 := Numerator[f[n]]; (* Generating the sequence : *) Table[a[n], {n, 2, 20}]
%t A101992 Accumulate[Table[(-1)^n/(n EulerPhi[n]),{n,2,30}]]//Numerator (* _Harvey P. Dale_, Mar 19 2023 *)
%Y A101992 Cf. A000010 (phi), A002618, A065484.
%K A101992 frac,nonn
%O A101992 2,3
%A A101992 Orges Leka (oleka(AT)students.uni-mainz.de), Dec 23 2004
%E A101992 More terms from _Amiram Eldar_, Jul 13 2019