cp's OEIS Frontend

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.

A361970 a(n) is the least number k such that the equation uphi(x) = k has exactly n solutions, or -1 if no such k exists, where uphi is the unitary totient function (A047994).

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%I A361970 #13 Apr 02 2023 08:27:28
%S A361970 5,1,2,6,8,12,36,156,24,552,168,48,96,420,120,192,3264,144,384,336,
%T A361970 1536,288,360,240,672,1200,3888,1080,4896,1584,480,576,7056,4992,864,
%U A361970 1872,1152,3120,960,2400,720,2520,30960,2688,19968,1680,1728,1920,2016,2304,12000
%N A361970 a(n) is the least number k such that the equation uphi(x) = k has exactly n solutions, or -1 if no such k exists, where uphi is the unitary totient function (A047994).
%C A361970 Is there any n for which a(n) = -1?
%H A361970 Amiram Eldar, <a href="/A361970/b361970.txt">Table of n, a(n) for n = 0..300</a>
%F A361970 A361967(a(n)) = n.
%t A361970 solnum[n_] :=  Length[invUPhi[n]]; seq[len_, kmax_] := Module[{s = Table[-1, {len}], c = 0, k = 1, ind}, While[k < kmax && c < len, ind = solnum[k] + 1; If[ind <= len && s[[ind]] < 0, c++; s[[ind]] = k]; k++]; s]; seq[50, 10^5] (* using the function invUPhi from A361966 *)
%Y A361970 The unitary version of A007374.
%Y A361970 Cf. A047994, A135347, A347771, A361966, A361967, A361968, A361969, A361971.
%K A361970 nonn
%O A361970 0,1
%A A361970 _Amiram Eldar_, Apr 01 2023