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A152677
Subsequence of odd terms in A000203 (sum-of-divisors function sigma), in the order in which they occur and with repetitions.
6
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
OFFSET
1,2
COMMENTS
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.
LINKS
FORMULA
a(n) = A000203(A028982(n)). - R. J. Mathar, Dec 12 2008
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
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Cf. A000203 (sigma = sum-of-divisors function), A152678 (even terms in A000203), A028982 (squares and twice the squares).
See A062700 and A023195 for the subsequence resp. subset of primes; A023194 for the indices of A000203 which yield these primes.
Cf. A002117.
Sequence in context: A086517 A346296 A332374 * A135374 A253582 A117589
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Dec 10 2008
EXTENSIONS
Extended by R. J. Mathar, Dec 12 2008
Edited and definition reworded by M. F. Hasler, Jan 08 2020
STATUS
approved