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 A300858 #14 Mar 30 2018 09:26:25
%S A300858 0,0,0,0,0,-1,0,1,1,-1,0,-1,0,1,2,4,0,-1,0,3,4,3,0,3,3,5,6,7,0,-5,0,
%T A300858 11,6,7,6,6,0,9,8,11,0,1,0,13,12,13,0,13,5,13,12,17,0,13,10,19,14,19,
%U A300858 0,5,0,21,18,26,12,11,0,23,18,15,0,25,0,25,24,27
%N A300858 a(n) = A243823(n) - A243822(n).
%C A300858 Consider numbers in the cototient of n, listed in row n of A121998. For composite n > 4, there are nondivisors m in the cototient, listed in row n of A133995. Of these m, there are two species. The first are m that divide n^e with integer e > 1, while the last do not divide n^e. These are listed in row n of A272618 and A272619, and counted by A243822(n) and A243823(n), respectively. This sequence is the difference between the latter and the former species of nondivisors in the cototient of n.
%C A300858 Since A045763(n) = A243822(n) + A243823(n), this sequence examines the balance of the two components among nondivisors in the cototient of n.
%C A300858 For positive n < 6 and for p prime, a(n) = a(p) = 0, thus a(A046022(n)) = 0.
%C A300858 For prime powers p^e, a(p^e) = A243823(p^e), since A243822(p^e) = 0, thus a(n) = A243823(n) for n in A000961.
%C A300858 Value of a(n) is generally nonnegative; a(n) is negative for n = {6, 10, 12, 18, 30}; a(30) = -5, but a(n) = -1 for the rest of the aforementioned numbers. These five numbers are a subset of A295523.
%H A300858 Michael De Vlieger, <a href="/A300858/b300858.txt">Table of n, a(n) for n = 1..10000</a>
%F A300858 a(n) = 1 + n - A000010(n) - 2*A010846(n) + A000005(n).
%e A300858 a(6) = -1 since the only nondivisor in the cototient of 6 is 4, which divides 6^e with e > 1; therefore 0 - 1 = -1.
%e A300858 a(8) = 1 since the only nondivisor in the cototient of 8 is 6, and 6 does not divide 8^e with e > 1, therefore 1 - 0 = 1.
%e A300858 Some values of a(n) and related sequences:
%e A300858 n a(n) A243823(n) A243822(n) A272619(n) A272618(n)
%e A300858 -------------------------------------------------------------
%e A300858 1 0 0 0 - -
%e A300858 2 0 0 0 - -
%e A300858 3 0 0 0 - -
%e A300858 4 0 0 0 - -
%e A300858 5 0 0 0 - -
%e A300858 6 -1 0 1 - {4}
%e A300858 7 0 0 0 - -
%e A300858 8 1 1 0 {6} -
%e A300858 9 1 1 0 {6} -
%e A300858 10 -1 1 2 {6} {4,8}
%e A300858 11 0 0 0 - -
%e A300858 12 -1 1 2 {10} {8,9}
%e A300858 13 0 0 0 - -
%e A300858 14 1 3 2 {6,10,12} {4,8}
%e A300858 15 2 3 1 {6,10,12} {9}
%e A300858 16 4 4 0 {6,10,12,14} -
%e A300858 17 0 0 0 - -
%e A300858 18 -1 3 4 {10,14,15} {4,8,12,16}
%e A300858 19 0 0 0 - -
%e A300858 20 3 5 2 {6,12,14,15,18} {8,16}
%e A300858 ...
%t A300858 f[n_] := Count[Range@ n, _?(PowerMod[n, Floor@ Log2@ n, #] == 0 &)]; Array[#1 - #3 + 1 - 2 #2 + #4 & @@ {#, f@ #, EulerPhi@ #, DivisorSigma[0, #]} &, 76]
%o A300858 (PARI) a(n) = 1 + n + numdiv(n) - eulerphi(n) - 2*sum(k=1, n, if(gcd(n,k)-1, 0, moebius(k)*(n\k))); \\ _Michel Marcus_, Mar 17 2018
%Y A300858 Cf. A000005, A000010, A000961, A010846, A046022, A121998, A133995, A173540, A243822, A243823, A272618, A272619, A295523, A300859, A300861.
%K A300858 sign
%O A300858 1,15
%A A300858 _Michael De Vlieger_, Mar 14 2018