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A231815
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Squarefree numbers (A005117) of the form p*q*r with prime factors p, q, r with q = 2*p-1 and r = 2*q-1.
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3
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30, 51319, 3882139, 289022911, 674910259, 991523479, 1893583519, 4550912389, 9761467669, 16721570539, 28685399311, 72886214809, 77372307511, 82720376839, 98685849571, 173850108931, 220038912319, 229352039821, 240313142749, 257401051861, 428178002569
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OFFSET
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1,1
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COMMENTS
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Squarefree numbers of the form p*q*r, where p < q < r = primes with q = 2*p - 1 and r = 2*q - 1; that is, r = 4*p - 3.
These numbers are divisible by the arithmetic mean of their proper divisors.
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LINKS
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EXAMPLE
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3882139 = 79*157*313; 157 = 2*79 - 1; 313 = 2*157 - 1.
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MATHEMATICA
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t = {}; p = 1; Do[While[p = NextPrime[p]; ! (PrimeQ[p2 = 2 p - 1] && PrimeQ[p3 = 2 p2 - 1])]; AppendTo[t, p*p2*p3], {30}]; t (* T. D. Noe, Nov 15 2013 *)
3#-10#^2+8#^3&/@Select[Prime[Range[600]], AllTrue[{2#-1, 4#-3}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 02 2016 *)
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CROSSREFS
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Cf. A057326 (first member of a prime triple in a 2p-1 progression).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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