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A152677
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Subsequence of odd terms in A000203 (sum-of-divisors function sigma), in the order in which they occur and with repetitions.
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6
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1, 3, 7, 15, 13, 31, 39, 31, 63, 91, 57, 93, 127, 195, 121, 171, 217, 133, 255, 403, 363, 183, 399, 465, 403, 399, 511, 819, 307, 847, 549, 381, 855, 961, 741, 1209, 931, 1023, 553, 1651, 921, 781, 1815, 1281, 1143, 1093, 1767, 1953, 871, 2223, 2821, 993, 1995
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OFFSET
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1,2
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COMMENTS
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Equivalently: subsequence of A000203 (sigma) with indices equal to a square or twice a square (A028982).
See A060657 for the set of odd values in the range of the sigma function, i.e., the list of odd values in ordered by increasing size and without repetitions.
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^3, where c = (16-10*sqrt(2))*zeta(3)/Pi^2 = 0.226276... . - Amiram Eldar, Nov 28 2023
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MATHEMATICA
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Select[DivisorSigma[1, Range[1000]], OddQ[#] &] (* Giovanni Resta, Jan 08 2020 *)
With[{max = 1000}, DivisorSigma[1, Union[Range[Sqrt[max]]^2, 2*Range[Sqrt[max/2]]^2]]] (* Amiram Eldar, Nov 28 2023 *)
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PROG
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(PARI) A152677_upto(lim)=apply(sigma, vecsort(concat(vector(sqrtint(lim\1), i, i^2), vector(sqrtint(lim\2), i, 2*i^2)))) \\ Gives [a(n) = sigma(k) with k = A028982(n) <= lim]. - Charles R Greathouse IV, Feb 15 2013, corrected by M. F. Hasler, Jan 08 2020
(Magma) [d:k in [1..1000]|IsOdd(d) where d is DivisorSigma(1, k)]; // Marius A. Burtea, Jan 09 2020
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CROSSREFS
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KEYWORD
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easy,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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