A385561 Numbers m such that (1/m) * Sum_{k=1..m} phi(k)/k is closer to 6/Pi^2 than it is for any number smaller than m, where phi is the Euler totient function (A000010).
1, 2, 3, 4, 6, 10, 12, 16, 22, 28, 36, 66, 96, 100, 126, 156, 190, 330, 430, 540, 820, 876, 1086, 1422, 10596, 10836, 18096, 35796, 55786, 69336, 111100, 168666, 284650, 905950, 1482300, 1745590, 2405560, 2661310, 4023306, 5869956, 17454580, 25670646, 51305346, 79969618, 211025650, 622626790
Offset: 1
Keywords
References
- József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, page 27.
- Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, Berlin, 1963.
Programs
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Mathematica
seq[lim_] := Module[{s = {}, sum = 0, dm = 1, d}, Do[sum += EulerPhi[k]/k; If[(d = Abs[sum/k - 6/Pi^2]) < dm, dm = d; AppendTo[s, k]], {k, 1, lim}]; s]; seq[10^5] -
PARI
list(lim) = {my(sm = 0, dm = 1, d); for(k = 1, lim, sm += eulerphi(k)/k; d = abs(sm/k - 6/Pi^2); if(d < dm, dm = d; print1(k, ", ")));}
Comments