cp's OEIS Frontend

A308690 Square array A(n,k), n >= 1, k >= 0, where A(n,k) = Sum_{d|n} d^(k*n/d - k + 1), read by antidiagonals.

%I A308690 #25 May 09 2021 02:51:05
%S A308690 1,1,3,1,3,4,1,3,4,7,1,3,4,9,6,1,3,4,13,6,12,1,3,4,21,6,24,8,1,3,4,37,
%T A308690 6,66,8,15,1,3,4,69,6,216,8,41,13,1,3,4,133,6,762,8,201,37,18,1,3,4,
%U A308690 261,6,2784,8,1289,253,68,12,1,3,4,517,6,10386,8,9225,2197,648,12,28
%N A308690 Square array A(n,k), n >= 1, k >= 0, where A(n,k) = Sum_{d|n} d^(k*n/d - k + 1), read by antidiagonals.
%H A308690 Seiichi Manyama, <a href="/A308690/b308690.txt">Antidiagonals n = 1..140, flattened</a>
%F A308690 L.g.f. of column k: -log(Product_{j>=1} (1 - j^k*x^j)^(1/j^k)).
%F A308690 A(p,k) = p+1 for prime p.
%e A308690 Square array begins:
%e A308690     1,  1,  1,   1,   1,    1,     1, ...
%e A308690     3,  3,  3,   3,   3,    3,     3, ...
%e A308690     4,  4,  4,   4,   4,    4,     4, ...
%e A308690     7,  9, 13,  21,  37,   69,   133, ...
%e A308690     6,  6,  6,   6,   6,    6,     6, ...
%e A308690    12, 24, 66, 216, 762, 2784, 10386, ...
%e A308690     8,  8,  8,   8,   8,    8,     8, ...
%t A308690 T[n_, k_] := DivisorSum[n, #^(k*n/# - k + 1) &]; Table[T[k, n - k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Amiram Eldar_, May 09 2021 *)
%Y A308690 Columns k=0..3 give A000203, A055225, A308688, A308689.
%Y A308690 Cf. A294579, A308509, A308694.
%K A308690 nonn,tabl
%O A308690 1,3
%A A308690 _Seiichi Manyama_, Jun 17 2019