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Search: id:A036913
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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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+0
7
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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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COMMENT
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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 (noe(AT)sspectra.com), Jun 14 2006
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REFERENCES
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Glyn Harman, On sparsely totient numbers, Glasgow Math. J. 33 (1991), 349-358.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..302
Roger C. Baker and Glyn Harman, Sparsely totient numbers, Annales de la faculte des sciences de Toulouse Ser. 6, 5 no. 2 (1996), 183-190.
D. W. Masser and P. Shiu, On sparsely totient numbers, Pacific J. Math. 121, no. 2 (1986), 407-426.
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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 (g_m(AT)mcraefamily.com), Feb 12 2009]
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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 (noe(AT)sspectra.com), Jun 14 2006
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CROSSREFS
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Cf. A097942 (highly totient numbers). Records in A006511 (see also A132154).
Sequence in context: A159793 A006511 A113274 this_sequence A117311 A125024 A053660
Adjacent sequences: A036910 A036911 A036912 this_sequence 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 (davidwwilson(AT)comcast.net)
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