cp's OEIS Frontend

A308694 Square array A(n,k), n >= 1, k >= 0, where A(n,k) = Sum_{d|n} d^(k*(n/d - 1)), read by antidiagonals.

%I A308694 #27 May 09 2021 02:50:53
%S A308694 1,1,2,1,2,2,1,2,2,3,1,2,2,4,2,1,2,2,6,2,4,1,2,2,10,2,9,2,1,2,2,18,2,
%T A308694 27,2,4,1,2,2,34,2,93,2,14,3,1,2,2,66,2,339,2,82,11,4,1,2,2,130,2,
%U A308694 1269,2,578,83,23,2,1,2,2,258,2,4827,2,4354,731,283,2,6
%N A308694 Square array A(n,k), n >= 1, k >= 0, where A(n,k) = Sum_{d|n} d^(k*(n/d - 1)), read by antidiagonals.
%H A308694 Seiichi Manyama, <a href="/A308694/b308694.txt">Antidiagonals n = 1..140, flattened</a>
%F A308694 L.g.f. of column k: -log(Product_{j>=1} (1 - j^k*x^j)^(1/j^(k+1))).
%F A308694 A(p,k) = 2 for prime p.
%e A308694 Square array begins:
%e A308694    1, 1,  1,  1,   1,    1,    1, ...
%e A308694    2, 2,  2,  2,   2,    2,    2, ...
%e A308694    2, 2,  2,  2,   2,    2,    2, ...
%e A308694    3, 4,  6, 10,  18,   34,   66, ...
%e A308694    2, 2,  2,  2,   2,    2,    2, ...
%e A308694    4, 9, 27, 93, 339, 1269, 4827, ...
%e A308694    2, 2,  2,  2,   2,    2,    2, ...
%t A308694 T[n_, k_] := DivisorSum[n, #^(k*(n/# - 1)) &]; Table[T[k, n - k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Amiram Eldar_, May 09 2021 *)
%Y A308694 Columns k=0..3 give A000005, A087909, A308692, A308693.
%Y A308694 Cf. A308509, A308690.
%K A308694 nonn,tabl
%O A308694 1,3
%A A308694 _Seiichi Manyama_, Jun 17 2019