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A349729
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Numbers k >= 1 such that A018804(k) + A000203(k) is a triangular number.
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0
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2, 4, 5, 7, 10, 33, 34, 38, 49, 60, 92, 116, 132, 155, 159, 220, 268, 285, 315, 360, 437, 472, 579, 602, 664, 722, 835, 1254, 1269, 1320, 1336, 1348, 1436, 1786, 1797, 1890, 1996, 2016, 2024, 2050, 2115, 2163, 2344, 2427, 2455, 2595, 2710, 2961, 3497
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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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k = 10 : A018804(10) = 27, A000203(10) = 18, 27 + 18 = 45 which is a triangular number thus 10 is a term.
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MATHEMATICA
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f1[p_, e_] := (p^(e + 1) - 1)/(p - 1); f2[p_, e_] := (e*(p - 1)/p + 1)*p^e; triQ[n_] := IntegerQ@Sqrt[8*n + 1]; q[n_] := triQ[Times @@ f1 @@@ (fct = FactorInteger[n]) + Times @@ f2 @@@ fct]; Select[Range[2, 3500], q] (* Amiram Eldar, Nov 27 2021 *)
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PROG
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(PARI) isok(k) = ispolygonal(sumdiv(k, d, k*eulerphi(d)/d) + sigma(k), 3); \\ Michel Marcus, Nov 27 2021
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CROSSREFS
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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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