A131883 - OEIS

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.

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