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

2,1

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000010, A061108.

Sequence in context: A096494 A116568 A239933 * A352928 A319399 A352434

Adjacent sequences: A061103 A061104 A061105 * A061107 A061108 A061109

Keyword

nonn

Author

Labos Elemer, May 29 2001

Status

approved