

A131883


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.


3



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
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OFFSET

1,2


COMMENTS

Conjecture: After omitting multiple occurrences we get A036912.  Vladeta Jovovic, 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.


LINKS

M. F. Hasler, Table of n, a(n) for n = 1..1000
Max Alekseyev, Proof of Jovovic's conjecture


EXAMPLE

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.


MAPLE

A131883 := proc(n) min(seq(numtheory[phi](i), i=n+1..2*n)) ; end: seq(A131883(n), n=1..500) ; # R. J. Mathar, Nov 09 2007


MATHEMATICA

Table[Min[Table[EulerPhi[i], {i, n + 1, 2*n}]], {n, 1, 80}] (* Stefan Steinerberger, Oct 30 2007 *)


PROG

(PARI) A131883(n)=vecsort(vector(n, i, eulerphi(n+i)))[1]
vector(300, i, A131883(i)) \\ M. F. Hasler, Nov 04 2007


CROSSREFS

Sequence in context: A297824 A281796 A072376 * A113452 A122461 A092533
Adjacent sequences: A131880 A131881 A131882 * A131884 A131885 A131886


KEYWORD

nonn


AUTHOR

Leroy Quet, Oct 24 2007


EXTENSIONS

More terms from Stefan Steinerberger and R. J. Mathar, Oct 30 2007


STATUS

approved



