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A048290 Numbers m that divide Sum_{k=1..m} phi(k). 19
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 (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)
Edward A. Bender, Oren Patashnik and Howard Rumsey, Jr., Pizza Slicing, Phi's and the Riemann Hypothesis, American Mathematical Monthly, Vol. 101 (1994), pp. 307-317.
FORMULA
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.
EXAMPLE
Euler sums are *1*, *2*, 4, 6, *10*, *12*, ..., *80*, ..., *510624*,... for n=1, 2, 3, 4, 5, 6, ..., 16, ...., 1296, ...
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
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 March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)