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%I #19 Mar 30 2024 03:01:18
%S 1,3,3,7,3,13,3,15,9,17,3,33,3,21,19,31,3,43,3,45,23,29,3,73,13,33,27,
%T 57,3,85,3,63,31,41,27,111,3,45,35,101,3,109,3,81,67,53,3,153,17,87,
%U 43,93,3,133,35,129,47,65,3,217,3,69,83,127,39,157,3,117,55,149,3,247,3,81,99,129,39,181,3,213,81,89,3,281
%N Sum of the even divisors of 2n, minus the (n-1)st odd number.
%C a(n) = 3 if and only if n is prime.
%F a(n) = A074400(n) - A005408(n-1) = 2*A000203(n) - 2*n + 1 = A000203(n) - A235796(n).
%F Sum_{k=1..n} a(k) = (Pi^2/6 - 1) * n^2 + O(n*log(n)). - _Amiram Eldar_, Mar 30 2024
%t a[n_] := 2*(DivisorSigma[1, n] - n) + 1; Array[a, 100] (* _Amiram Eldar_, Mar 30 2024 *)
%o (PARI) a(n) = 2*sigma(n) - 2*n + 1; \\ _Michel Marcus_, Oct 29 2017
%Y Partial sums give A294016.
%Y Cf. A000203, A013661, A005408, A074400, A235796, A294017.
%K nonn
%O 1,2
%A _Omar E. Pol_, Oct 28 2017
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