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A125237
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Numbers n for which the absolute value of the abundance of both n and n^2 is a prime number.
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3
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3, 9, 10, 18, 50, 100, 104, 121, 136, 289, 464, 576, 650, 900, 5041, 6962, 7225, 10201, 14400, 55225, 65025, 87025, 102152, 147456, 171698, 174050, 179776, 182329, 189225, 201601, 222784, 291848, 312481, 380689, 410881, 469225, 481636, 488601
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OFFSET
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1,1
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LINKS
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EXAMPLE
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n=3: The abundance of 3 is -2, the negative of a prime. n^2=9, the abundance of 9 is -5, the negative of a prime as well.
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MATHEMATICA
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pQ[n_] := PrimeQ[DivisorSigma[1, n] - 2n]; Select[Range[10^4], pQ[#] && pQ[#^2] &] (* Amiram Eldar, Sep 24 2019 *)
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PROG
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(PARI) {for(n=1, 500000, if(isprime(abs(sigma(n)-2*n)) && isprime(abs(sigma(n^2)-2*n^2)), print1(n, ", ")))} \\ Klaus Brockhaus, Nov 25 2006
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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