A131883 - OEIS

%I #20 Aug 26 2015 01:10:48

%S 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,

%T 12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,16,16,16,16,16,16,16,16,

%U 16,16,16,16,20,20,20,20,20,20,24,24,24,24,24,24,24,24,24,24,24,24,24,24

%N 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.

%C Conjecture: After omitting multiple occurrences we get A036912. - _Vladeta Jovovic_, Oct 31 2007. This conjecture has been established by _Max Alekseyev_ - see link below.

%C 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.

%H M. F. Hasler, <a href="/A131883/b131883.txt">Table of n, a(n) for n = 1..1000</a>

%H Max Alekseyev, <a href="/A131883/a131883.txt">Proof of Jovovic's conjecture</a>

%e 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.

%p 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

%t Table[Min[Table[EulerPhi[i], {i, n + 1, 2*n}]], {n, 1, 80}] (* _Stefan Steinerberger_, Oct 30 2007 *)

%o (PARI) A131883(n)=vecsort(vector(n,i,eulerphi(n+i)))[1]

%o vector(300,i,A131883(i)) \\ _M. F. Hasler_, Nov 04 2007

%K nonn

%O 1,2

%A _Leroy Quet_, Oct 24 2007

%E More terms from _Stefan Steinerberger_ and _R. J. Mathar_, Oct 30 2007