

A036913


Sparsely totient numbers; numbers n such that m > n implies phi(m) > phi(n).


8



2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630, 660, 690, 840, 870, 1050, 1260, 1320, 1470, 1680, 1890, 2310, 2730, 2940, 3150, 3570, 3990, 4620, 4830, 5460, 5610, 5670, 6090, 6930, 7140, 7350, 8190, 9240, 9660
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OFFSET

1,1


COMMENTS

The paper by Masser and Shiu lists 150 terms of this sequence less than 10^6. For odd prime p, they show that p# and p*p# are in this sequence, where p# denotes the primorial (A002110).  T. D. Noe, Jun 14 2006


REFERENCES

Glyn Harman, On sparsely totient numbers, Glasgow Math. J. 33 (1991), 349358.


LINKS

T. D. Noe, Table of n, a(n) for n = 1..5000
Roger C. Baker and Glyn Harman, Sparsely totient numbers, Annales de la faculte des sciences de Toulouse Ser. 6, 5 no. 2 (1996), 183190.
D. W. Masser and P. Shiu, On sparsely totient numbers, Pacific J. Math. 121, no. 2 (1986), 407426.


EXAMPLE

This sequence contains 60 because of all the numbers whose totient is <=16, 60 is the largest such number. [From Graeme McRae, Feb 12 2009]


MATHEMATICA

nn=10000; lastN=Table[0, {nn}]; Do[e=EulerPhi[n]; If[e<=nn, lastN[[e]]=n], {n, 10nn}]; mx=0; lst={}; Do[If[lastN[[i]]>mx, mx=lastN[[i]]; AppendTo[lst, mx]], {i, Length[lastN]}]; lst  T. D. Noe, Jun 14 2006


CROSSREFS

Cf. A097942 (highly totient numbers). Records in A006511 (see also A132154).
Sequence in context: A006511 A113274 A181660 * A117311 A125024 A178480
Adjacent sequences: A036910 A036911 A036912 * A036914 A036915 A036916


KEYWORD

nonn


AUTHOR

David W. Wilson


STATUS

approved



