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A083253 Smallest number k for which abs(A045763(k) - A073757(k)) = n, i.e., signed difference of size of related and unrelated sets to k equals either n or -n.

%I A083253 #19 Aug 01 2017 05:37:09
%S A083253 30,1,2,3,4,5,8,7,16,21,32,11,64,13,84,27,78,17,200,19,90,57,140,23,
%T A083253 102,69,120,435,114,29,132,31,126,93,392,81,138,37,156,49,230,41,168,
%U A083253 43,322,129,260,47,150,77,180,795,186,53,204,95,198,885,280,59,434,61,228,183
%N A083253 Smallest number k for which abs(A045763(k) - A073757(k)) = n, i.e., signed difference of size of related and unrelated sets to k equals either n or -n.
%C A083253 a(258) > 10^5. - _Michael De Vlieger_, Jul 31 2017
%H A083253 Michael De Vlieger, <a href="/A083253/b083253.txt">Table of n, a(n) for n = 0..257</a>
%F A083253 a(n) = min{x; abs(A045763(x) - A073757(x)) = n}.
%F A083253 a(p) = p, for p prime.
%e A083253 A045763(x) - A073757(x) = 0 is first satisfied at x = 30 = a(0).
%t A083253 With[{s = Table[Abs[n - 2 (DivisorSigma[0, n] + EulerPhi[n] - 1)], {n, 10^3}]}, TakeWhile[#, # > 0 &] &@ Flatten@ Map[FirstPosition[s, #] /. k_ /; MissingQ@ k -> 0 &, Range[0, Max@ s]]] (* _Michael De Vlieger_, Jul 31 2017 *)
%o A083253 (PARI) a(n) = {my(k = 1); while (abs(k - 2*(numdiv(k) + eulerphi(k) - 1)) != n, k++); k;} \\ _Michel Marcus_, Aug 01 2017
%Y A083253 Cf. A000005, A000010, A045763, A073757, A083243-A083249, A083250, A083251, A083252.
%K A083253 nonn
%O A083253 0,1
%A A083253 _Labos Elemer_, May 07 2003