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A066100 Primes p such that their square p^2 has a sum of cube of divisors which is prime. +0
3
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 (list; graph; listen)
OFFSET

1,1

COMMENT

It appears that squares of these primes give A063783, those numbers whose sum of cube of divisors is prime.

LINKS

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

FORMULA

Divisor[3, p^2]=q, where both p and q are primes.

EXAMPLE

p=11: p^2=121, cube of divisors of p^2 ={p^6, p^3, 1}, sigma3[p^2]=p^6+p^3+1=1771561+1331+1=1772893=q, a prime.

PROGRAM

(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)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 13 2009]

CROSSREFS

Cf. A001158, A000040, A063783.

Sequence in context: A042337 A061482 A135161 this_sequence A029497 A109809 A096456

Adjacent sequences: A066097 A066098 A066099 this_sequence A066101 A066102 A066103

KEYWORD

nonn,new

AUTHOR

Labos E. (labos(AT)ana.sote.hu), Dec 04 2001

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.


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