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 A083546 The geometric mean of the Euler totient function of 2 consecutive integers {k, k+1} when it is an integer. 4
 1, 2, 8, 12, 48, 48, 60, 80, 96, 128, 144, 180, 280, 240, 240, 288, 288, 288, 336, 288, 384, 360, 480, 480, 640, 720, 672, 600, 576, 720, 720, 720, 672, 864, 960, 864, 960, 1080, 1008, 1408, 1296, 960, 1008, 1320, 1260, 1056, 1440, 1200, 1728, 1440, 1296 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = sqrt(A000010(x) * A000010(x+1)) = sqrt(phi(x) * phi(x+1)) = sqrt(A083542(x)) where x = A083545(n). EXAMPLE 12 is a term since sqrt(phi(19) * phi(20)) = sqrt(18 * 8) = sqrt(144) = 12. MATHEMATICA f[x_] := EulerPhi[x]; Do[s=Sqrt[f[n+1]*f[n]]; If[IntegerQ[s], Print[s]], {n, 1, 5000}] Select[Sqrt[#]&/@(Times@@@Partition[EulerPhi[Range[3000]], 2, 1]), IntegerQ] (* Harvey P. Dale, Nov 04 2020 *) CROSSREFS Cf. A000010, A083542, A083542, A066813, A058515, A083542, A083545. Sequence in context: A104039 A135443 A280092 * A013190 A176968 A308935 Adjacent sequences: A083543 A083544 A083545 * A083547 A083548 A083549 KEYWORD nonn AUTHOR Labos Elemer, May 21 2003 STATUS approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)