login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A308704 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where A(n,k) is Sum_{d|n} d^(k*d+1). 3
1, 1, 3, 1, 9, 4, 1, 33, 82, 7, 1, 129, 2188, 1033, 6, 1, 513, 59050, 262177, 15626, 12, 1, 2049, 1594324, 67108993, 48828126, 280026, 8, 1, 8193, 43046722, 17179869697, 152587890626, 13060696236, 5764802, 15, 1, 32769, 1162261468, 4398046513153, 476837158203126, 609359740069674, 4747561509944, 134218761, 13 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
L.g.f. of column k: -log(Product_{j>=1} (1 - x^j)^(j^(k*j))).
G.f. of column k: Sum_{j>=1} j^(k*j+1) * x^j/(1 - x^j).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
3, 9, 33, 129, 513, ...
4, 82, 2188, 59050, 1594324, ...
7, 1033, 262177, 67108993, 17179869697, ...
6, 15626, 48828126, 152587890626, 476837158203126, ...
MATHEMATICA
T[n_, k_] := DivisorSum[n, #^(k*# + 1) &]; Table[T[k, n - k], {n, 1, 9}, {k, 1, n}] // Flatten (* Amiram Eldar, May 09 2021 *)
CROSSREFS
Columns k=0..3 give A000203, A283498, A283533, A283535.
Row n=1..2 give A000012, A087289.
Sequence in context: A067417 A187887 A016577 * A270702 A124573 A127550
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jun 18 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)