|
%I #19 May 11 2021 01:55:06
%S 1,1,3,1,5,4,1,9,10,9,1,17,28,25,6,1,33,82,81,26,24,1,65,244,289,126,
%T 80,8,1,129,730,1089,626,330,50,41,1,257,2188,4225,3126,1604,344,161,
%U 37,1,513,6562,16641,15626,8634,2402,833,163,68,1,1025,19684,66049,78126,49100,16808,5249,973,290,12
%N Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{d|n} d^(n/d + k).
%H Seiichi Manyama, <a href="/A308502/b308502.txt">Antidiagonals n = 1..140, flattened</a>
%F L.g.f. of column k: -log(Product_{j>=1} (1 - j*x^j)^(j^(k-1))).
%e Square array begins:
%e 1, 1, 1, 1, 1, 1, ...
%e 3, 5, 9, 17, 33, 65, ...
%e 4, 10, 28, 82, 244, 730, ...
%e 9, 25, 81, 289, 1089, 4225, ...
%e 6, 26, 126, 626, 3126, 15626, ...
%e 24, 80, 330, 1604, 8634, 49100, ...
%t T[n_, k_] := DivisorSum[n, #^(n/# + k) &]; Table[T[k, n - k], {n, 1, 11}, {k, 1, n}] // Flatten (* _Amiram Eldar_, May 11 2021 *)
%Y Columns k=0..2 give A055225, A078308, A296601.
%Y Cf. A279394, A308504.
%K nonn,tabl
%O 1,3
%A _Seiichi Manyama_, Jun 02 2019
|
