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A065146
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Arithmetic, geometric and harmonic means of Phi[m] and Sigma[m] are all integers.
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3
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1, 248, 264, 418, 477, 1485, 3080, 3135, 3596, 3828, 5396, 10098, 12648, 20026, 21318, 22152, 23374, 24882, 35074, 35343, 39105, 41656, 44660, 49938, 55154, 56536, 61344, 71145, 74613, 86304, 87087, 104931, 118296, 124605, 129504
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,500
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FORMULA
| a = (Phi[m]+Sigma[m])/2, g = Sqrt[Phi[m]*Sigma[m]], h = (2*Phi[m]*Sigma[m])/(Phi[m]+Sigma[m]) = g^2/a are integers; Phi[] = A000010(), Sigma[] = A000203().
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EXAMPLE
| m = 5396, Phi[m] = 2520,Sigma[m] = 10080,A-mean = 6300, G-mean = 5040,H-mean = 4032; 65 cases below 1 million.
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MATHEMATICA
| Do[s = EulerPhi[n]*DivisorSigma[1, n]; z = (EulerPhi[n]+DivisorSigma[1, n])/2; u = h[n]; If[IntegerQ[Sqrt[s]]&&IntegerQ[z]&&IntegerQ[u], Print[n]], {n, 1, 1000000}]
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PROG
| (PARI) { n=0; for (m=1, 10^9, e=eulerphi(m); s=sigma(m); if (!issquare(e*s), next); h=(2*e*s)/(e + s); if (frac(h) != 0, next); if (frac((e + s)/2) != 0, next); write("b065146.txt", n++, " ", m); if (n==500, return) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 12 2009]
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CROSSREFS
| Cf. A000010, A000203, A062354, A011257.
Sequence in context: A001243 A048901 A187398 * A064977 A068400 A109478
Adjacent sequences: A065143 A065144 A065145 * A065147 A065148 A065149
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Oct 18 2001
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