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A347076
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Numbers m such that tau(m) = tau(m-1) + tau(m+1) and simultaneously sigma(m) = sigma(m-1) + sigma(m+1).
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1
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89484, 167784, 8587065618, 24033737496, 41249560520, 161721015522, 206958258156, 441151731162, 600656241732, 1013494535238, 4648478084262, 5099258875122, 7897343836494, 21060284613738, 26847208137084
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OFFSET
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1,1
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COMMENTS
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a(n) is even. If a(n) is odd then two consecutive numbers are perfect squares. This only happens with (0, 1) which does not give terms. - David A. Corneth, Aug 16 2021
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LINKS
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EXAMPLE
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tau(89484) = tau(89483) + tau(89485); 12 = 4 + 8.
sigma(89484) = sigma(89483) + sigma(89485); 208824 = 91608 + 117216.
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MATHEMATICA
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Select[Range[200000], DivisorSigma[{0, 1}, # - 1] + DivisorSigma[{0, 1}, # + 1] - DivisorSigma[{0, 1}, # ] == {0, 0} &] (* Amiram Eldar, Aug 16 2021 *)
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PROG
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(Magma) [m: m in [2..10^5] | #Divisors(m) eq #Divisors(m - 1) + #Divisors(m + 1) and &+Divisors(m) eq &+Divisors(m - 1) + &+Divisors(m + 1)]
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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