

A119434


Odd n such that 2*phi(n) < n.


4



105, 165, 195, 315, 495, 525, 585, 735, 825, 945, 975, 1155, 1365, 1485, 1575, 1755, 1785, 1815, 1995, 2145, 2205, 2415, 2475, 2535, 2625, 2805, 2835, 2925, 3003, 3045, 3135, 3255, 3315, 3465, 3675, 3705, 3795, 3885, 3927, 4095, 4125, 4305, 4389, 4455
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OFFSET

1,1


COMMENTS

Obviously 2*phi(n) = n is impossible for odd n. Odd elements of A054741 and A119432. This is not the same as A036798. 684411 = 3*7*13*23*109 is in this sequence but not in A036798. (This is may not be the smallest such value.) The primitive elements of this sequence are A119433, excluding the initial 2
If n is in the sequence, then so is every odd multiple of n.  Robert Israel, Jan 06 2017
The asymptotic density of this sequence is in the interval (0.01120, 0.01176) (Kobayashi, 2016). It is 1/2 less than the asymptotic density of A119432. The number of terms below 10^k for k = 3, 4, ... are 11, 109, 1152, 11076, 111927, 1124091, 11224403, 112074112, ...  Amiram Eldar, Oct 15 2020


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
Mitsuo Kobayashi, A generalization of a series for the density of abundant numbers, International Journal of Number Theory, Vol. 12, No. 3 (2016), pp. 671677.


FORMULA

A036798 UNION A118700.  R. J. Mathar, Aug 08 2007
A119432 \ A299174.  Amiram Eldar, Oct 15 2020


MAPLE

select(t > numtheory:phi(t) < t/2, [seq(t, t=1..10000, 2)]);


MATHEMATICA

Select[Range[1, 10^4, 2], 2 EulerPhi[#] < #&] (* JeanFrançois Alcover, Apr 12 2019 *)


PROG

(PARI) lista(nn) = forstep (n=1, nn, 2, if (n > 2*eulerphi(n), print1(n, ", "))) \\ Michel Marcus, Jul 04 2015


CROSSREFS

Cf. A000010, A036798, A054741, A118700, A119432, A119433, A299174.
Sequence in context: A189936 A076762 A036798 * A091495 A256673 A308779
Adjacent sequences: A119431 A119432 A119433 * A119435 A119436 A119437


KEYWORD

nonn


AUTHOR

Franklin T. AdamsWatters, May 19 2006


STATUS

approved



