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%I #13 Sep 15 2023 02:26:49
%S 6,30,60,90,210,420,630,840,2310,4620,6930,9240,30030,60060,90090,
%T 510510,9699690,19399380,29099070,38798760,48498450,58198140,67897830,
%U 77597520,87297210,96996900,223092870,446185740,669278610,892371480
%N Numbers k which, for some r, are r-digit maximizers of k/phi(k).
%C I can show that for r > 1, the first r-digit term of the sequence is the smallest r-digit primorial, if it exists. It remains to investigate the first terms when existence fails. It is also not hard to see that for r > 1, the r-digit terms are in arithmetic progression with common difference equal to the smallest r-digit term. For example, 210, 420, 630, 840 are in arithmetic progression with common difference 210. Obviously the r-digit minimizer of k/phi(k) is the largest prime of k digits.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a065/065800.java">Java program</a> (github).
%e 30/phi(30) = 15/4 is maximal for two-digit numbers.
%e 210/phi(210) = 35/8 is maximal for three-digit numbers.
%Y Cf. A000010, A002110, A065657.
%K nonn,more
%O 1,1
%A _Joseph L. Pe_, Dec 05 2001
%E a(13)-a(15) corrected and a(16)-a(30) from _Sean A. Irvine_, Sep 15 2023