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A048290
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Numbers m that divide Sum_{k=1..m} phi(k).
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19
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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, 2258200198, 2438160726
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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Sum_{k=1..m} phi(k) is about (3/Pi^2)*m^2 [cf. A002088, first formula].
Not obviously infinite; rough heuristics predict about 3/2 log(N) terms less than N, log(N) even ones and log(N)/2 odd ones.
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EXAMPLE
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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
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s = 0; Do[s = s + EulerPhi[n]; If[IntegerQ[s/n], Print[n]], {n, 1, 10^8}]
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PROG
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(PARI) list(lim)=my(v=List(), s); for(k=1, lim, s+=eulerphi(k); if(s%k==0, listput(v, k))); Vec(v) \\ Charles R Greathouse IV, Feb 07 2017
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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