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 A219930 n such that phi(n) represents a new lower bound for the phi function. 2
 1, 3, 8, 14, 20, 36, 48, 66, 70, 96, 126, 132, 156, 240, 252, 300, 336, 450, 480, 540, 660, 690, 714, 870, 900, 1080, 1320, 1470, 1530, 1710, 1950, 2340, 2940, 2970, 3360, 3780, 4200, 4830, 5040, 5610, 5670, 5880, 6270, 7140, 7350, 7410, 8400, 9660, 9870 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: If n is in the sequence, then the sequence contains an infinite number of multiples of n. Conjecture: Except for 1 and 3, all members of the sequence are even. If n is odd, it cannot be squarefree. Conjecture: There does not exist N such that for all n > N, a(n) is divisible by 30. A036912 gives the values of the phi function at these n. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 EXAMPLE phi(1)=1, and for n>=1, phi(n)>=1. phi(3)=2, and for n>=3, phi(n)>=2. phi(8)=4, and for n>=8, phi(n)>=4. phi(14)=6, and for n>=14, phi(n)>=6. MATHEMATICA nn = 8!; t = Table[EulerPhi[n], {n, nn}]; min = Infinity; t2 = {}; Do[If[t[[n]] <= min, AppendTo[t2, {n, t[[n]]}]; min = t[[n]]], {n, Length[t], 1, -1}]; t2 = Reverse[t2]; t3 = {}; mx = 0; Do[If[i[[2]] > mx, mx = i[[2]]; AppendTo[t3, i[[1]]]], {i, t2}]; t3 (* T. D. Noe, Dec 04 2012 *) PROG (JavaScript) p = new Array(); p[0] = NaN; p[1] = 2; p[2] = 3; mj = 2; for (k = 3; k < 50000; k += 2) makeprimes(k); function makeprimes(i) { for (j = 2; j <= mj; j++) if (i%p[j] == 0) return false; p[++mj] = i; return true; } function primeFactorize(n) { var pf = new Array(), pc, pfc; pf[0] = new Array(); pf[1] = new Array(); pc = 1; pfc = -1; while (n != 1) { if (n%p[pc] == 0) {pfc++; pf[0][pfc] = p[pc]; pf[1][pfc] = 0; } while (n%p[pc] == 0) {n /= p[pc]; pf[1][pfc]++; } pc++; } return pf; } function phi(n) { var f, i, v; v = 1; f = primeFactorize(n); for (i = 0; i < f[0].length; i++) v *= Math.pow(f[0][i], f[1][i] - 1)*(f[0][i] - 1); return v; } function isMin(arr, ik, k) { var i, im; im = true; for (i = ik; i < arr.length; i++) if (arr[i] < k) {im = false; break; } return im; } phiV = new Array(); for (k = 1; k < 50000; k++) phiV[k] = phi(k); cm = 1; for (n = 1; n < 3000; n++) if (phiV[n] > cm && isMin(phiV, n, phiV[n])) {cm = phiV[n]; document.write(n + ", "); } CROSSREFS Cf. A000010, A036912, A057635, A014197. Sequence in context: A299647 A063617 A062550 * A333962 A366087 A022947 Adjacent sequences: A219927 A219928 A219929 * A219931 A219932 A219933 KEYWORD nonn AUTHOR Jon Perry, Dec 01 2012 STATUS approved

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