A061106 Compute Euler totient function for the prime(n+1)-prime(n)-1 composite numbers between two consecutive primes; choose the smallest.

2, 2, 4, 4, 6, 6, 8, 8, 8, 12, 16, 12, 20, 16, 18, 16, 20, 24, 24, 24, 32, 24, 24, 40, 32, 48, 36, 40, 32, 48, 40, 44, 48, 40, 48, 54, 80, 48, 56, 48, 60, 64, 84, 60, 48, 72, 96, 72, 88, 72, 64, 80, 72, 84, 80, 72, 88, 96, 92, 96, 80, 120, 96, 144, 80, 96, 108, 112, 120, 116

Offset: 2

Author

Labos Elemer, May 29 2001

Keywords

• nonn

Examples

			p(30)=113 is followed by 13 composites; phi of these are {36, 88, 56, 72, 58, 96, 32, 110, 60, 80, 60, 100, 36}, the smallest of which is 32=a(30) and the largest is 110.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A000010, A061108.

Programs

Mathematica

Min[EulerPhi[Range[First[#]+1,Last[#]-1]]]&/@Partition[Prime[Range[ 2,80]],2,1]  (* Harvey P. Dale, Aug 18 2011 *)
Table[Min[EulerPhi[Range[Prime[i], Prime[i+1]]]], {i, 2, 100}] (* T. D. Noe, Aug 18 2011 *)

PARI

{ n=1; q=3; m=10^6; forprime (p=5, prime(1003), a=m; for (i=q + 1, p - 1, a=min(eulerphi(i), a)); q=p; write("b061106.txt", n++, " ", a) ) } \\ Harry J. Smith, Jul 18 2009

Formula

a(n) = Min{phi(c) : prime(n) < c < prime(n+1)}.