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A065116
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Numbers k such that sigma(k) + tau(k) and sigma(k) - tau(k) are primes.
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1
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8, 162, 512, 32768, 41472, 3748322, 5120000, 6837602, 8000000, 35701250, 75031250, 78125000, 91125000, 907039232, 10660336128, 11911961250, 21234895362, 41265473762, 55965865922, 209642370242, 835707290112, 1148179179938, 1821331173888, 2097152000000
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OFFSET
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1,1
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COMMENTS
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Terms must be twice a square (see A064205).
No terms are congruent to 4 or 6 (mod 10) (see A064205). (End)
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LINKS
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EXAMPLE
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162 is a term since sigma(162) = 363 and tau(162) = 10 are numbers whose sum (373) and difference (353) are both primes.
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MATHEMATICA
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Do[ds1 = DivisorSigma[1, n]; ds0 = DivisorSigma[0, n]; If[ PrimeQ[ds1 + ds0] && PrimeQ[ds1 - ds0], Print[n]], {n, 1, 10^7} ]
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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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