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A294614
Sum of the divisors of 12*n - 1, divided by 12, minus n.
1
0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 2, 3, 0, 0, 0, 3, 4, 0, 0, 0, 0, 8, 4, 3, 0, 3, 6, 0, 0, 5, 0, 7, 4, 0, 0, 0, 18, 0, 0, 0, 0, 9, 4, 12, 4, 0, 14, 0, 0, 5, 8, 11, 0, 0, 6, 0, 12, 9, 0, 5, 0, 13, 6, 5, 10, 7, 14, 0, 0, 5, 0, 31, 0, 5, 0, 7, 30, 0, 12, 0, 0, 17, 6, 0, 0, 13, 18, 9, 8
OFFSET
1,8
COMMENTS
a(n) = 0 iff n is in A138620.
First occurrence of k > -1: 1, 3, 8, 13, 18, 31, 28, 33, 23, 43, 66, 53, 45, 63, 48, 101, 166, etc.
FORMULA
a(n) = sigma(12*n-1)/12 - n = A000203(A017653(n-1))/12 - n.
Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/18 - 1/2 = 0.048311... . - Amiram Eldar, Mar 28 2024
EXAMPLE
a(13) = 3 since d(12*13-1)/12 - 13 = 192/12 - 13 = 16 - 13 = 3.
MATHEMATICA
a[n_] := DivisorSigma[1, 12 n - 1]/12 - n; Array[a, 90]
PROG
(PARI) a(n) = sigma(12*n-1)/12 - n;
CROSSREFS
Inspired by A291900.
Sequence in context: A160812 A338271 A176866 * A347403 A063918 A271419
KEYWORD
nonn,easy
AUTHOR
STATUS
approved