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%I #13 Sep 08 2022 08:46:18
%S 2,1,5,7,27,11,13,58,17,19,55,23,65,106,29,31,85,142,37,158,41,43,115,
%T 47,119,125,53,133,145,59,61,254,262,67,274,71,73,298,1180,79,187,83,
%U 203,346,89,209,235,382,97,394,101,103,169,107,109,253,113,458,295
%N a(n) = smallest number k such that floor(phi(k)/tau(k)) = n.
%C a(n) = the smallest number k such that floor(A000010(k)/A000005(k)) = A279507(k) = n.
%C Sequences b_n of numbers k such that floor(phi(k)/tau(k)) = n for n = 0..2:
%C b_0: 2, 4, 6, 12;
%C b_1: 1, 3, 8, 10, 14, 16, 18, 20, 24, 30, 36, 42, 48, 60;
%C b_2: 5, 9, 15, 22, 28, 32, 40, 54, 66, 72, 84, 90, 96, 120, 180.
%C Sequences b_n are finite for all n >=0. See A279509 (largest number k such that floor(phi(k)/tau(k)) = n).
%C Supersequence of A045344 (primes excluding 3).
%F a((p-1)/2) = p for p = prime > 3.
%e For n = 2; a(2) = 5 because 5 is the smallest number with floor(phi(5) / tau(5)) = floor(4/2) = 2.
%t Table[k = 1; While[Floor[EulerPhi[k]/DivisorSigma[0, k]] != n, k++]; k, {n, 0, 58}] (* _Michael De Vlieger_, Dec 14 2016 *)
%o (Magma) [Min([n: n in[1..100000] | Floor(EulerPhi(n)/NumberOfDivisors(n)) eq k]): k in [0..60]]
%o (PARI) a(n) = my(k=1); while(floor((eulerphi(k)/numdiv(k)))!=n, k++); k \\ _Felix Fröhlich_, Dec 14 2016
%Y Cf. A000005, A000010, A020488, A020490, A045344, A279289, A279507, A279509.
%K nonn
%O 0,1
%A _Jaroslav Krizek_, Dec 13 2016
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