|
|
A081307
|
|
a(n) = (n+1)*tau(n) - sigma(n).
|
|
4
|
|
|
1, 3, 4, 8, 6, 16, 8, 21, 17, 26, 12, 50, 14, 36, 40, 54, 18, 75, 20, 84, 56, 56, 24, 140, 47, 66, 72, 118, 30, 176, 32, 135, 88, 86, 96, 242, 38, 96, 104, 238, 42, 248, 44, 186, 198, 116, 48, 366, 93, 213, 136, 220
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Old name was: Sum_{k=1..n} Sum_{m=1..k} 1/(1-x^m).
Number of positive integer pairs (s,t) with s <= t <= n, such that s|n. For example, when n = 6, the 16 pairs are (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,3), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (6,6). - Wesley Ivan Hurt, Nov 15 2021
|
|
LINKS
|
|
|
FORMULA
|
Sum_{k=1..n} Sum_{m=1..k} 1/(1-x^m).
|
|
MATHEMATICA
|
Table[(n + 1) DivisorSigma[0, n] - DivisorSigma[1, n], {n, 100}] (* Wesley Ivan Hurt, Nov 15 2021 *)
|
|
PROG
|
(PARI) a(n)=if(n<1, 0, polcoeff(sum(k=1, n, sum(l=1, k, 1/(1-x^l)), x*O(x^n)), n))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|