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A232355
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Numbers n such that sigma(triangular(n)) = sigma(n)^2.
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2
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1, 11, 695, 991, 2839, 3707, 9347, 10703, 12847, 27089, 42251, 56419, 74671, 115289, 168739, 191051, 219295, 233729, 280111, 300731, 326899, 353651, 430859, 611799, 642991, 661715, 1035827, 1116607, 1181579, 1234519, 1365491, 1485035, 1777099, 1854671, 1905875
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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11 is in the sequence because sigma(11*12/2) = sigma(66) = 144 = 12^2 = sigma(11)^2.
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MATHEMATICA
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Select[Range@1000000, DivisorSigma[1, #]^2==DivisorSigma[1, (# (# + 1)/2)] &] (* Vincenzo Librandi, Jun 13 2015 *)
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PROG
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(PARI) isok(n) = sigma(n)^2 == sigma(n*(n+1)/2); \\ Michel Marcus, Nov 23 2013
(Magma) [n: n in [1..7*10^5] | SumOfDivisors(n*(n+1) div 2) eq SumOfDivisors(n)^2]; // Vincenzo Librandi, Jun 13 2015
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CROSSREFS
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Cf. A000203 (sigma(n): sum of divisors of n), A000217 (triangular(n): = n*(n+1)/2).
Cf. A116990 (indices of triangular numbers whose sum of divisors is square).
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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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