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%I #19 Jan 09 2017 10:06:12
%S 1,1,2,1,3,2,1,5,4,3,1,9,10,7,2,1,17,28,21,6,4,1,33,82,73,26,12,2,1,
%T 65,244,273,126,50,8,4,1,129,730,1057,626,252,50,15,3,1,257,2188,4161,
%U 3126,1394,344,85,13,4,1,513,6562,16513,15626,8052,2402,585,91,18,2,1,1025,19684,65793,78126,47450,16808,4369,757,130,12,6
%N Triangle read by rows, T(n,m) = sigma_{n-m}(m) for n >= 1, m = 1,2, ..., n.
%C See A109974 (downward antidiagonals) for details and references. sigma_k(n) is the sum of the k-th power of the positive divisors of n.
%C This is the triangle read by rows obtained from the array sigma_k(n) for k >= 0, n >= 1, read by upward antidiagonals.
%C The row sums are A108639.
%F T(n, m) = sigma_{n-m}(m), n >= 1, m = 1..n.
%e The triangle T(n, m) begins:
%e n\m 1 2 3 4 5 6 7 8 9 10
%e 1: 1
%e 2: 1 2
%e 3: 1 3 2
%e 4: 1 5 4 3
%e 5: 1 9 10 7 2
%e 6: 1 17 28 21 6 4
%e 7: 1 33 82 73 26 12 2
%e 8: 1 65 244 273 126 50 8 4
%e 9: 1 129 730 1057 626 252 50 15 3
%e 10: 1 257 2188 4161 3126 1394 344 85 13 4
%e ...
%e n = 11: 1 513 6562 16513 15626 8052 2402 585 91 18 2,
%e n = 12: 1 1025 19684 65793 78126 47450 16808 4369 757 130 12 6.
%e ...
%p T := (n, k) -> numtheory:-sigma[n-k](k):
%p seq(seq(T(n,k), k=1..n), n=1..12); # _Peter Luschny_, Jan 07 2017
%t Table[DivisorSigma[k, #] &[n - k + 1], {n, 0, 11}, {k, n, 0, -1}] (* _Michael De Vlieger_, Jan 09 2017 *)
%Y Cf. A109974, A108639.
%K nonn,tabl,easy
%O 1,3
%A _Wolfdieter Lang_, Jan 07 2017
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