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A063783 Sum of cube of divisors is prime. 4
4, 9, 121, 36481, 72361, 146689, 259081, 654481, 683929, 786769, 1985281, 2036329, 3193369, 3636649, 3798601, 4583881, 5031049, 5470921, 5555449, 6135529, 6713281, 7284601, 7778521 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

FORMULA

Solutions to DivisorSigma[3, x]=prime.

EXAMPLE

All these terms are squares of primes (2, 3, 11, 191, 269, 383, 509, 809, 827, 887, 1409, 1427, 1787, 1907, 1949, 2141, 2243, 2339, 2357, 2477, 2591, 2699, 2789), so their DivisorSigma[3, p^2] = p^6+p^3+1 has polynomial of degree 6.

sigma[3,9]=1+27+729=757, a prime.

MATHEMATICA

Select[Prime[Range[500]]^2, PrimeQ@ DivisorSigma[3, #] &] (* Michael De Vlieger, Jul 16 2017 *)

PROG

(PARI) { n=0; p=0; for (m=1, 10^9, p=nextprime(p+1); if(isprime(p^6 + p^3 + 1), write("b063783.txt", n++, " ", p^2); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 31 2009

CROSSREFS

Cf. A023194, A066100, A001158.

Sequence in context: A048411 A225739 A065379 * A168138 A267898 A324981

Adjacent sequences:  A063780 A063781 A063782 * A063784 A063785 A063786

KEYWORD

nonn

AUTHOR

Labos Elemer, Aug 17 2001

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)