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Numbers n such that sigma_6(n)/sigma_2(n) is prime.
1

%I #8 Dec 24 2016 21:16:05

%S 2,3,5,13,17,31,43,61,83,109,131,229,239,257,263,269,311,313,443,463,

%T 503,571,593,599,619,641,647,653,659,701,797,811,853,953,967,1009,

%U 1031,1039,1063,1123,1373,1459,1483,1499,1663,1669,1693,1733,1741,1759,1789

%N Numbers n such that sigma_6(n)/sigma_2(n) is prime.

%H Harry J. Smith, <a href="/A065820/b065820.txt">Table of n, a(n) for n=1..1000</a>

%e All entries are themselves prime.

%t Select[Range[1, 2000 ], PrimeQ[( DivisorSigma[6, # ])/DivisorSigma[2, # ]] & ]

%o (PARI) { n=0; for (m=1, 10^9, f=sigma(m, 6)/sigma(m, 2); if (frac(f) == 0 && isprime(f), write("b065820.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Oct 31 2009

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Dec 06 2001