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Search: id:A065405
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| A065405 |
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Composite numbers n such that the sum of the divisors of n^2 is a prime. |
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9
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| 4, 8, 27, 49, 64, 125, 169, 256, 289, 512, 529, 729, 841, 1849, 2197, 3125, 4913, 5329, 6241, 6889, 15625, 16129, 29791, 32768, 37249, 51529, 57121, 69169, 76729, 113569, 117649, 128881, 139129, 157609, 192721, 208849, 226981, 229441, 253009
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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All these composite numbers m should be prime powers because if m=a.b with GCD[a,b]=1, then Sigma[aabb]=Sigma[aa]*Sigma[bb] cannot be a prime; 46 from 236 prime-powers below 1000000 are here.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,70
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FORMULA
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Sigma[A065405(n)^2] = Sigma[A065404(n)] = A065403(n) is prime.
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MATHEMATICA
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Select[ Range[3 10^5], ! PrimeQ[ # ] && PrimeQ[ DivisorSigma[1, #^2]] & ]
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PROGRAM
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(PARI) { n=0; for (m=1, 10^9, if (isprime(m), next); x=sigma(m^2); if (isprime(x), write("b065405.txt", n++, " ", m); if (n==70, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 18 2009]
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CROSSREFS
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Cf. A062700, A000203, A065403-A065405, A053182, A053183, A028982.
Sequence in context: A012982 A012952 A100411 this_sequence A026085 A036720 A110132
Adjacent sequences: A065402 A065403 A065404 this_sequence A065406 A065407 A065408
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 06 2001
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