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 A279508 a(n) = smallest number k such that floor(phi(k)/tau(k)) = n. 2
 2, 1, 5, 7, 27, 11, 13, 58, 17, 19, 55, 23, 65, 106, 29, 31, 85, 142, 37, 158, 41, 43, 115, 47, 119, 125, 53, 133, 145, 59, 61, 254, 262, 67, 274, 71, 73, 298, 1180, 79, 187, 83, 203, 346, 89, 209, 235, 382, 97, 394, 101, 103, 169, 107, 109, 253, 113, 458, 295 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n) = the smallest number k such that floor(A000010(k)/A000005(k)) = A279507(k) = n. Sequences b_n of numbers k such that floor(phi(k)/tau(k)) = n for n = 0..2: b_0: 2, 4, 6, 12; b_1: 1, 3, 8, 10, 14, 16, 18, 20, 24, 30, 36, 42, 48, 60; b_2: 5, 9, 15, 22, 28, 32, 40, 54, 66, 72, 84, 90, 96, 120, 180. Sequences b_n are finite for all n >=0. See A279509 (largest number k such that floor(phi(k)/tau(k)) = n). Supersequence of A045344 (primes excluding 3). LINKS FORMULA a((p-1)/2) = p for p = prime > 3. EXAMPLE For n = 2; a(2) = 5 because 5 is the smallest number with floor(phi(5) / tau(5)) = floor(4/2) = 2. MATHEMATICA Table[k = 1; While[Floor[EulerPhi[k]/DivisorSigma[0, k]] != n, k++]; k, {n, 0, 58}] (* Michael De Vlieger, Dec 14 2016 *) PROG (MAGMA)  [Min([n: n in[1..100000] | Floor(EulerPhi(n)/NumberOfDivisors(n)) eq k]): k in [0..60]] (PARI) a(n) = my(k=1); while(floor((eulerphi(k)/numdiv(k)))!=n, k++); k \\ Felix FrÃ¶hlich, Dec 14 2016 CROSSREFS Cf. A000005, A000010, A020488, A020490, A045344, A279289, A279507, A279509. Sequence in context: A175002 A088014 A193662 * A175770 A268950 A141507 Adjacent sequences:  A279505 A279506 A279507 * A279509 A279510 A279511 KEYWORD nonn AUTHOR Jaroslav Krizek, Dec 13 2016 STATUS approved

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Last modified August 7 19:57 EDT 2020. Contains 336279 sequences. (Running on oeis4.)