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A036913
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Sparsely totient numbers; numbers n such that m > n implies phi(m) > phi(n).
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11
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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
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1,1
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COMMENTS
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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
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LINKS
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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.
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EXAMPLE
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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)
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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)
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MATHEMATICA
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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
Union@ FoldList[Max, Values[#][[All, -1]]] &@ KeySort@ PositionIndex@ EulerPhi@ Range[10^4] (* Michael De Vlieger, Jun 06 2017, Version 10 *)
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CROSSREFS
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Cf. A097942 (highly totient numbers). Records in A006511 (see also A132154).
Sequence in context: A325708 A113274 A181660 * A317089 A117311 A125024
Adjacent sequences: A036910 A036911 A036912 * A036914 A036915 A036916
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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