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A065403
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Primes of form sigma(m^2) where m is composite number.
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9
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31, 127, 1093, 2801, 8191, 19531, 30941, 131071, 88741, 524287, 292561, 797161, 732541, 3500201, 5229043, 12207031, 25646167, 28792661, 39449441, 48037081, 305175781, 262209281, 917087137, 2147483647, 1394714501, 2666986681
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,100
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EXAMPLE
| 46 cases below 10^12. All Mersenne primes are here: sigma[(2^((p-1)/2))^2]=sigma[(2^(p-1)]=-1 +2^p, for suitable p.
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MATHEMATICA
| Do[s=DivisorSigma[1, n]; If[PrimeQ[s]&&!PrimeQ[Sqrt[n]], Print[{n, Sqrt[n], s}]], {n, 1, 20000000}]
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PROG
| (PARI) { n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), write("b065403.txt", n++, " ", x); if (n==100, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 18 2009]
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CROSSREFS
| Cf. A062700, A000203, A001348, A065403-A065405.
Sequence in context: A158563 A079141 A049203 * A035502 A183838 A043355
Adjacent sequences: A065400 A065401 A065402 * A065404 A065405 A065406
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Nov 06 2001
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