

A066100


Primes p such that p^6 + p^3 + 1 is prime.


4



2, 3, 11, 191, 269, 383, 509, 809, 827, 887, 1409, 1427, 1787, 1907, 1949, 2141, 2243, 2339, 2357, 2477, 2591, 2699, 2789, 4073, 4517, 4643, 4787, 5171, 5237, 5501, 5531, 5693, 6311, 6329, 6359, 6911, 6947, 7019, 7253, 7349, 7499, 7577, 7691, 7907, 8819
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OFFSET

1,1


COMMENTS

Original name: "Primes p such that the sum of the cubes of the divisors of p^2 is prime."
It appears that squares of these primes give A063783, those numbers whose sum of cubes of divisors is prime.


LINKS

Harry J. Smith, Table of n, a(n) for n=1..1000


FORMULA

Primes p such that sigma_3(p^2) is prime.


EXAMPLE

p=11: p^2=121, cubes of divisors of p^2 = {p^6, p^3, 1}, sigma_3(p^2) = p^6 + p^3 + 1 = 1771561 + 1331 + 1 = 1772893 = q, a prime.


MATHEMATICA

Select[Prime@ Range@ 1200, PrimeQ@ DivisorSigma[3, #^2] &] (* Michael De Vlieger, Jul 16 2017 *)


PROG

(PARI) { n=0; for (m=1, 10^9, p=prime(m); if (isprime(sigma(p^2, 3)), write("b066100.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Nov 13 2009


CROSSREFS

Cf. A000040, A001158, A063783.
Sequence in context: A177854 A273598 A135161 * A029497 A318130 A109809
Adjacent sequences: A066097 A066098 A066099 * A066101 A066102 A066103


KEYWORD

nonn


AUTHOR

Labos Elemer, Dec 04 2001


EXTENSIONS

Name replaced with simpler description offered in an Oct 10 2010 comment by James R. Buddenhagen by Jon E. Schoenfield, Jul 17 2017


STATUS

approved



