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 A101993 #16 Jul 13 2019 04:45:51
%S A101993 4,6,7,9,10,13,16,21,27,35,39,41,45,48,52,76,84,94,119,150,165,190,
%T A101993 251,260,264,306,416,428,488,513,521,523,553,615,622,640,711,714,765,
%U A101993 797,807,888,967,1146,1292,1555,1602,1750,1822,1859,1868,1950,2009,2059
%N A101993 Indices k for which the numerator of Sum_{i=2..k} ( (-1)^i/(i * phi(i)) ) is a prime number.
%H A101993 Amiram Eldar, <a href="/A101993/b101993.txt">Table of n, a(n) for n = 1..100</a>
%e A101993 a(1) = 4 because numerator of Sum_{i=2..4} ((-1)^i/(i * phi(i))) is 11 and 11 is a prime number.
%t A101993 (* Defining the sum: *) f[n_Integer] /; n >= 2 := Sum[(-1)^(i)/(i EulerPhi[i]), {i, 2, n}] (* Generating the sequence: *) PhiPrimes[n_Integer] /; n >= 2 := Flatten[Table[If[PrimeQ[Numerator[f[i]]], i, {}], {i, 2, n}]] (* Checking if a given n is a phi-prime: *) PhiPrimeQ[n_Integer] /; n >= 2 := If[PrimeQ[ Numerator[f[n]]], Numerator[f[n]], "not a phi-prime"]
%t A101993 Select[Range[2, 1300], PrimeQ[Numerator[Sum[(-1)^i/(i*EulerPhi[i]), {i, 2, #}]]] &] (* _Stefan Steinerberger_, Apr 02 2006 *)
%o A101993 (PARI) isok(n) = isprime(numerator(sum(k=2, n, (-1)^k/(k*eulerphi(k))))); \\ _Michel Marcus_, Aug 27 2015
%Y A101993 Cf. A000010 (Euler's totient function phi(n)).
%Y A101993 Cf. A101992 (the sequence of the numerator of the sum described in the name of the current sequence).
%K A101993 nonn
%O A101993 1,1
%A A101993 Orges Leka (oleka(AT)students.uni-mainz.de), Dec 23 2004
%E A101993 More terms from _Stefan Steinerberger_, Apr 02 2006
%E A101993 More terms from _Amiram Eldar_, Jul 13 2019