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Search: id:A065150
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| A065150 |
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Harmonic mean of Phi[n] and Sigma[n] is an integer. |
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+0
1
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| 1, 12, 15, 35, 56, 78, 95, 140, 143, 172, 190, 248, 264, 287, 315, 319, 323, 357, 418, 477, 588, 594, 675, 812, 814, 840, 899, 910, 1045, 1107, 1118, 1131, 1199, 1208, 1254, 1349, 1420, 1425, 1485, 1495, 1558, 1608, 1672, 1763, 2214, 2261, 2318, 2337
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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Mod[G^2, A] = 0, where G^2=A000010(m)*A000203(m), A=[A000010(m)+A000203(m)]/2; harmonic mean =[G^2]/A is integer.
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EXAMPLE
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m=319, Phi[319]=280, Sigma[319]=360; Phi[319]*Sigma[319]=100800, Phi[319]+Sigma[319]=640; 1/harmonic mean =[640/100800]/2, harmonic mean=315, arithmetic mean=320, geometric mean is not an integer.
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PROGRAM
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(PARI) { n=0; for (m=1, 10^9, e=eulerphi(m); s=sigma(m); h=(2*e*s)/(e + s); if (frac(h) == 0, write("b065150.txt", n++, " ", m); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 13 2009]
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CROSSREFS
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A000010, A000203, A065146, A011257.
Sequence in context: A124521 A134221 A161917 this_sequence A087098 A109315 A024875
Adjacent sequences: A065147 A065148 A065149 this_sequence A065151 A065152 A065153
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 18 2001
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