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Search: id:A131883
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| A131883 |
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a(n) = the minimum value from among (phi(n+1),phi(n+2),phi(n+3),...,phi(2n)), where phi(m) (A000010) is the number of positive integers which are coprime to m and are <= m. |
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+0
3
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| 1, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 20, 20, 20, 20, 20, 20, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: After omitting multiple occurrences we get A036912. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 31 2007. This conjecture has been established by Max Alekseyev - see link below.
The Alekseyev link establishes the following explicit relationship between A131883, A036912 and A057635. Namely, for t belonging to A036912, we have t=A131883(A057635(t)-1). In other words, A036912(n) = A131883(A057635(A036912(n))-1) for all n.
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LINKS
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M. F. Hasler, Table of n, a(n) for n = 1..1000
Leroy Quet, Home Page (listed in lieu of email address)
Max Alekseyev, Proof of Jovovic's conjecture
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EXAMPLE
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For n = 6 we have phi(7)=6, phi(8)=4, phi(9)=6, phi(10)=4, phi(11)=10, phi(12)=4. The least of these values is 4. So a(6) = 4.
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MAPLE
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A131883 := proc(n) min(seq(numtheory[phi](i), i=n+1..2*n)) ; end: seq(A131883(n), n=1..500) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 09 2007
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MATHEMATICA
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Table[Min[Table[EulerPhi[i], {i, n + 1, 2*n}]], {n, 1, 80}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 30 2007
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PROGRAM
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(PARI/gp program from M. F. Hasler, maximilian.hasler(AT)gmail.com, Nov 04 2007)
A131883(n)=vecsort(vector(n, i, eulerphi(n+i)))[1]
vector(300, i, A131883(i))
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CROSSREFS
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Sequence in context: A080217 A157901 A072376 this_sequence A113452 A122461 A092533
Adjacent sequences: A131880 A131881 A131882 this_sequence A131884 A131885 A131886
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Oct 24 2007
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2007
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