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A325423
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Numbers k such that sigma(2*k+1) >= sigma(2*k).
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1
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1, 7, 31, 37, 67, 73, 97, 103, 127, 157, 199, 202, 229, 241, 247, 262, 277, 283, 307, 313, 331, 337, 346, 367, 379, 382, 397, 409, 427, 457, 472, 487, 499, 517, 547, 562, 577, 607, 619, 643, 661, 667, 682, 697, 727, 757, 769, 787
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OFFSET
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1,2
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COMMENTS
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The function A(x) enumerating the terms not exceeding x has the property that lim_{x->oo} A(x)/x exists (Hildebrand, 1990).
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REFERENCES
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M. Laub, Advanced Problems: 6555. The American Mathematical Monthly, 94(8), 800 (1987). doi:10.2307/2323430.
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LINKS
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FORMULA
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a(n) ~ c*n with 18.2 < c < 18.6 (claimed by Kobayashi and Trudgian).
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EXAMPLE
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7 is in the sequence because sigma(14) = 1+2+7+14 = 24 <= sigma(15) = 1+3+5+15 = 24;
31 is in the sequence because sigma(62) = 1+2+31+62 = 96 <= sigma(63) = 1+3+7+9+21+63 = 104.
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MATHEMATICA
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Position[Partition[DivisorSigma[1, Range[2, 1601]], 2], _?(#[[2]] >= #[[1]]&), 1, Heads->False]//Flatten (* Harvey P. Dale, Jan 10 2022 *)
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PROG
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(PARI) isok(n) = sigma(2*n+1) >= sigma(2*n); \\ Michel Marcus, Sep 09 2019
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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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