OFFSET
1,2
LINKS
T. D. Noe, Rows n=1..100, flattened
Eric Weisstein's World of Mathematics, Divisor Function
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.
From R. J. Mathar, Oct 29 2006: (Start)
EXAMPLE
From R. J. Mathar:
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...
MAPLE
T:= (n, k)-> numtheory[sigma][k](n):
seq(seq(T(n, k), k=0..n-1), n=1..10); # Alois P. Heinz, Oct 25 2024
MATHEMATICA
T[n_, k_] := DivisorSigma[k, n];
Table[T[n, k], {n, 1, 10}, {k, 0, n-1}] // Flatten (* Jean-François Alcover, Dec 16 2021 *)
CROSSREFS
KEYWORD
AUTHOR
Reinhard Zumkeller, May 21 2003
EXTENSIONS
Corrected by R. J. Mathar, Dec 05 2006
STATUS
approved