

A061106


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


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,1


LINKS

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


FORMULA

a(n) = Min{Phi(c) : prime(n+1)>c>prime(n)}.


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 * A319399 A161764 A293706
Adjacent sequences: A061103 A061104 A061105 * A061107 A061108 A061109


KEYWORD

nonn


AUTHOR

Labos Elemer, May 29 2001


STATUS

approved



