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A048290 Numbers m that divide Sum_{k=1..m} phi(k).

%I A048290 #57 Feb 13 2024 06:57:03
%S A048290 1,2,5,6,16,25,36,249,617,1296,13763,76268,189074,783665,1102394,
%T A048290 3258466,3808854,7971034,15748051,27746990,41846733,153673168,
%U A048290 195853251,302167272,402296412,732683468,807656448,844492262,848152352,1122039882,2258200198,2438160726
%N A048290 Numbers m that divide Sum_{k=1..m} phi(k).
%C A048290 The odd terms of this sequence and A063986 are the same. - _Jud McCranie_, Jun 26 2005
%H A048290 Donovan Johnson, <a href="/A048290/b048290.txt">Table of n, a(n) for n = 1..37</a> (terms < 10^12)
%H A048290 Edward A. Bender, Oren Patashnik and Howard Rumsey, Jr., <a href="http://www.jstor.org/stable/2975623">Pizza Slicing, Phi's and the Riemann Hypothesis</a>, American Mathematical Monthly, Vol. 101 (1994), pp. 307-317.
%H A048290 D. Rusin, <a href="https://web.archive.org/web/20060111010021/http://www.math-atlas.org/99/euler_phi">Euler phi function</a>
%F A048290 Sum_{k=1..m} phi(k) is about (3/Pi^2)*m^2 [cf. A002088, first formula].
%F A048290 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.
%e A048290 Euler sums are *1*, *2*, 4, 6, *10*, *12*, ..., *80*, ..., *510624*,... for n=1, 2, 3, 4, 5, 6, ..., 16, ...., 1296, ...
%t A048290 s = 0; Do[s = s + EulerPhi[n]; If[IntegerQ[s/n], Print[n]], {n, 1, 10^8}]
%o A048290 (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
%Y A048290 Cf. A000010, A002088. See A063986 for n divides Sum_{k=1..n} k-phi(k).
%K A048290 nonn,nice
%O A048290 1,2
%A A048290 _David J. Rusin_
%E A048290 10 more terms computed by _Dean Hickerson_
%E A048290 One more term from _Robert G. Wilson v_, Sep 07 2001
%E A048290 More terms from _Naohiro Nomoto_, Mar 22 2002
%E A048290 5 more terms from _Jud McCranie_, Jun 21 2005