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A378640 Smallest m such that phi(m) does not divide n, where phi is the Euler totient function (A000010).

%I A378640 #14 Dec 06 2024 11:31:52
%S A378640 3,5,3,7,3,5,3,7,3,5,3,11,3,5,3,7,3,5,3,7,3,5,3,11,3,5,3,7,3,5,3,7,3,
%T A378640 5,3,11,3,5,3,7,3,5,3,7,3,5,3,11,3,5,3,7,3,5,3,7,3,5,3,15,3,5,3,7,3,5,
%U A378640 3,7,3,5,3,11,3,5,3,7,3,5,3,7,3,5,3,11,3,5
%N A378640 Smallest m such that phi(m) does not divide n, where phi is the Euler totient function (A000010).
%C A378640 Up to n = 10^7 the distinct terms of the sequence (which are also the record values) are {3, 5, 7, 11, 15, 17, 19, 23, 29, 47, 51, 53}. Is this A076245 (for n >= 2)?
%C A378640 First differs from A095366 at n = 60.
%C A378640 It appears that a(n) = A095366(n) except when n = 60*(2*k + 1), with k >= 0, where a(n) = 15 while A095366(n) = 17.
%H A378640 Paolo Xausa, <a href="/A378640/b378640.txt">Table of n, a(n) for n = 1..10000</a>
%F A378640 a(n) = 3 if n is odd.
%t A378640 A378640[n_] := If[OddQ[n], 3, Module[{m = 4}, While[Divisible[n, EulerPhi[++m]]]; m]];
%t A378640 Array[A378640, 100]
%Y A378640 Cf. A000010, A076245, A095366, A378638, A378641, A378642.
%K A378640 nonn,easy
%O A378640 1,1
%A A378640 _Paolo Xausa_, Dec 05 2024