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A048290
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Numbers n such that n divides Sum_{k=1..n} phi(k).
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11
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1, 2, 5, 6, 16, 25, 36, 249, 617, 1296, 13763, 76268, 189074, 783665, 1102394, 3258466, 3808854, 7971034, 15748051, 27746990, 41846733, 153673168, 195853251, 302167272, 402296412, 732683468, 807656448, 844492262, 848152352, 1122039882
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The odd terms of A048290 and A063986 are the same. - Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Jun 26 2005
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REFERENCES
| Bender, Patashnik and Rumsey, Pizza Slicing, Phis and the Riemann Hypothesis, American Mathematical Monthly, Vol. 101 (1994), pp. 307-317.
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LINKS
| Donovan Johnson, Table of n, a(n) for n = 1..37 (terms < 10^12)
D. Rusin, Euler phi function
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FORMULA
| The sum to n is about (3/pi^2)*n^2.
Not obviously infinite; rough heuristics predict about 3/2 log(N) such n's less than N, log(N) even ones and log(N)/2 odd ones.
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EXAMPLE
| Euler-sums are *1*, *2*, 4, 6, *10*, *12*, ..., *80*, ..., *510624*,... for n=1, 2, 3, 4, 5, 6, ..., 16, ...., 1296, ...
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MATHEMATICA
| s = 0; Do[s = s + EulerPhi[n]; If[IntegerQ[s/n], Print[n]], {n, 1, 10^8}]
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CROSSREFS
| Cf. A000010, A002088. See A063986 for n divides Sum_{k=1..n} k-phi(k).
Sequence in context: A037079 A101325 A042980 * A029939 A082198 A098871
Adjacent sequences: A048287 A048288 A048289 * A048291 A048292 A048293
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KEYWORD
| nonn,nice
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AUTHOR
| Dave Rusin (rusin(AT)math.niu.edu)
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EXTENSIONS
| 10 more terms computed by Dean Hickerson (dean.hickerson(AT)yahoo.com)
One more term from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 07 2001
More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Mar 22 2002
5 more terms from Jud McCranie (JudMcCranie(AT)ugaalum.uga.edu), Jun 21 2005
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