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A294015
Sum of the even divisors of 2n, minus the (n-1)st odd number.
5
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, 57, 3, 85, 3, 63, 31, 41, 27, 111, 3, 45, 35, 101, 3, 109, 3, 81, 67, 53, 3, 153, 17, 87, 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
OFFSET
1,2
COMMENTS
a(n) = 3 if and only if n is prime.
FORMULA
a(n) = A074400(n) - A005408(n-1) = 2*A000203(n) - 2*n + 1 = A000203(n) - A235796(n).
Sum_{k=1..n} a(k) = (Pi^2/6 - 1) * n^2 + O(n*log(n)). - Amiram Eldar, Mar 30 2024
MATHEMATICA
a[n_] := 2*(DivisorSigma[1, n] - n) + 1; Array[a, 100] (* Amiram Eldar, Mar 30 2024 *)
PROG
(PARI) a(n) = 2*sigma(n) - 2*n + 1; \\ Michel Marcus, Oct 29 2017
CROSSREFS
Partial sums give A294016.
Sequence in context: A323774 A062402 A347405 * A156838 A274845 A324048
KEYWORD
nonn
AUTHOR
Omar E. Pol, Oct 28 2017
STATUS
approved