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
Conjecture: Except for 2 and 18, all terms are Zumkeller numbers (A083207). Verified for the first 1800 terms. - Ivan N. Ianakiev, Sep 04 2022
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 Faculté des Sciences de Toulouse Ser. 6, 5 no. 2 (1996), 183-190.
Glyn Harman, On sparsely totient numbers, Glasgow Math. J. 33 (1991), 349-358.
D. W. Masser and P. Shiu, On sparsely totient numbers, Pacific J. Math. 121, no. 2 (1986), 407-426.
Michael De Vlieger, Largest k such that A002110(k) | a(n) and A287352(a(n)).
Michael De Vlieger, First term m > prime(n)^2 in A036913 such that gcd(prime(n), m) = 1.
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]
From Michael De Vlieger, Jun 25 2017: (Start)
Positions of primorials A002110(k) in a(n):
n k a(n) = A002110(k)
----------------------------------
1 1 2
2 2 6
5 3 30
13 4 210
31 5 2310
69 6 30030
136 7 510510
231 8 9699690
374 9 223092870
578 10 6469693230
836 11 200560490130
1169 12 7420738134810
1591 13 304250263527210
2149 14 13082761331670030
2831 15 614889782588491410
3667 16 32589158477190044730
4661 17 1922760350154212639070
(End)
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
KEYWORD
nonn
AUTHOR
STATUS
approved