A152677 - OEIS

%I #35 Nov 28 2023 11:00:41

%S 1,3,7,15,13,31,39,31,63,91,57,93,127,195,121,171,217,133,255,403,363,

%T 183,399,465,403,399,511,819,307,847,549,381,855,961,741,1209,931,

%U 1023,553,1651,921,781,1815,1281,1143,1093,1767,1953,871,2223,2821,993,1995

%N Subsequence of odd terms in A000203 (sum-of-divisors function sigma), in the order in which they occur and with repetitions.

%C Equivalently: subsequence of A000203 (sigma) with indices equal to a square or twice a square (A028982).

%C 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.

%H Amiram Eldar, <a href="/A152677/b152677.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000203(A028982(n)). - _R. J. Mathar_, Dec 12 2008

%F 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

%t Select[DivisorSigma[1, Range[1000]], OddQ[#] &] (* _Giovanni Resta_, Jan 08 2020 *)

%t With[{max = 1000}, DivisorSigma[1, Union[Range[Sqrt[max]]^2, 2*Range[Sqrt[max/2]]^2]]] (* _Amiram Eldar_, Nov 28 2023 *)

%o (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

%o (Magma) [d:k in [1..1000]|IsOdd(d) where d is DivisorSigma(1,k)]; // _Marius A. Burtea_, Jan 09 2020

%Y Cf. A000203 (sigma = sum-of-divisors function), A152678 (even terms in A000203), A028982 (squares and twice the squares).

%Y See A062700 and A023195 for the subsequence resp. subset of primes; A023194 for the indices of A000203 which yield these primes.

%Y Cf. A002117.

%K easy,nonn

%O 1,2

%A _Omar E. Pol_, Dec 10 2008

%E Extended by _R. J. Mathar_, Dec 12 2008

%E Edited and definition reworded by _M. F. Hasler_, Jan 08 2020