|
|
A082771
|
|
Triangular array, read by rows: t(n,k) = Sum(d^k: d|n), 0<=k<n.
|
|
7
|
|
|
1, 2, 3, 2, 4, 10, 3, 7, 21, 73, 2, 6, 26, 126, 626, 4, 12, 50, 252, 1394, 8052, 2, 8, 50, 344, 2402, 16808, 117650, 4, 15, 85, 585, 4369, 33825, 266305, 2113665, 3, 13, 91, 757, 6643, 59293, 532171, 4785157, 43053283, 4, 18, 130, 1134, 10642, 103158, 1015690, 10078254, 100390882, 1001953638
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
t(n, k) = Product(((p^((e(n, p)+1)*k))-1)/(p^k-1): n=Product(p^e(n, p): p prime)), 0<=k<n.
|
|
EXAMPLE
|
The triangle may be extended to a rectangular array (A319278):
1 1 1 1 1 1 1 1 1 1 1 ...
2 3 5 9 17 33 65 129 257 513 1025 ...
2 4 10 28 82 244 730 2188 6562 19684 59050 ...
3 7 21 73 273 1057 4161 16513 65793 262657 1049601 ...
2 6 26 126 626 3126 15626 78126 390626 1953126 9765626 ...
4 12 50 252 1394 8052 47450 282252 1686434 10097892 60526250 ...
2 8 50 344 2402 16808 117650 823544 5764802 40353608 282475250 ...
4 15 85 585 4369 33825 266305 2113665 16843009 134480385 1074791425 ...
3 13 91 757 6643 59293 532171 4785157 43053283 387440173 3486843451 ...
4 18 130 1134 10642 103158 1015690 10078254 100390882 1001953638...
|
|
MATHEMATICA
|
T[n_, k_] := DivisorSigma[k, n];
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|