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
Keywords
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
Programs
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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 *)
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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)}.