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 A048290 Numbers n such that n divides Sum_{k=1..n} phi(k). 14
 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; text; internal format)
 OFFSET 1,2 COMMENTS The odd terms of this sequence and A063986 are the same. - Jud McCranie, Jun 26 2005 LINKS Donovan Johnson, Table of n, a(n) for n = 1..37 (terms < 10^12) Bender, Patashnik and Rumsey, Pizza Slicing, Phi's and the Riemann Hypothesis, American Mathematical Monthly, Vol. 101 (1994), pp. 307-317. D. Rusin, Euler phi function 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. EXAMPLE Euler-sums are *1*, *2*, 4, 6, *10*, *12*, ..., *80*, ..., *510624*,... for n=1, 2, 3, 4, 5, 6, ..., 16, ...., 1296, ... MAPLE with(numtheory); A048290:=proc(q) local a, n; a:=0; for n from 1 to q do a:=a+phi(n); if type(a/n, integer) then print(n); fi; od; end: A048290(10^10); # Paolo P. Lava, Mar 27 2013 MATHEMATICA s = 0; Do[s = s + EulerPhi[n]; If[IntegerQ[s/n], Print[n]], {n, 1, 10^8}] PROG (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 CROSSREFS Cf. A000010, A002088. See A063986 for n divides Sum_{k=1..n} k-phi(k). Sequence in context: A037079 A101325 A042980 * A306885 A029939 A082198 Adjacent sequences:  A048287 A048288 A048289 * A048291 A048292 A048293 KEYWORD nonn,nice AUTHOR EXTENSIONS 10 more terms computed by Dean Hickerson One more term from Robert G. Wilson v, Sep 07 2001 More terms from Naohiro Nomoto, Mar 22 2002 5 more terms from Jud McCranie, Jun 21 2005 STATUS approved

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Last modified September 29 21:59 EDT 2020. Contains 337432 sequences. (Running on oeis4.)