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A279394 Triangle read by rows, T(n,m) = sigma_{n-m}(m) for n >= 1, m = 1,2, ..., n.

%I A279394 #19 Jan 09 2017 10:06:12
%S A279394 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 A279394 65,244,273,126,50,8,4,1,129,730,1057,626,252,50,15,3,1,257,2188,4161,
%U A279394 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 A279394 Triangle read by rows, T(n,m) = sigma_{n-m}(m) for n >= 1,  m = 1,2, ..., n.
%C A279394 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 A279394 This is the triangle read by rows obtained from the array sigma_k(n) for k >= 0, n >= 1, read by upward antidiagonals.
%C A279394 The row sums are A108639.
%F A279394 T(n, m) = sigma_{n-m}(m), n >= 1, m = 1..n.
%e A279394 The triangle T(n, m) begins:
%e A279394 n\m 1   2    3    4    5    6   7  8  9 10
%e A279394 1:  1
%e A279394 2:  1   2
%e A279394 3:  1   3    2
%e A279394 4:  1   5    4    3
%e A279394 5:  1   9   10    7    2
%e A279394 6:  1  17   28   21    6    4
%e A279394 7:  1  33   82   73   26   12   2
%e A279394 8:  1  65  244  273  126   50   8  4
%e A279394 9:  1 129  730 1057  626  252  50 15  3
%e A279394 10: 1 257 2188 4161 3126 1394 344 85 13  4
%e A279394 ...
%e A279394 n = 11: 1 513 6562 16513 15626 8052 2402 585 91 18 2,
%e A279394 n = 12: 1 1025 19684 65793 78126 47450 16808 4369 757 130 12 6.
%e A279394 ...
%p A279394 T := (n, k) -> numtheory:-sigma[n-k](k):
%p A279394 seq(seq(T(n,k), k=1..n), n=1..12); # _Peter Luschny_, Jan 07 2017
%t A279394 Table[DivisorSigma[k, #] &[n - k + 1], {n, 0, 11}, {k, n, 0, -1}] (* _Michael De Vlieger_, Jan 09 2017 *)
%Y A279394 Cf. A109974, A108639.
%K A279394 nonn,tabl,easy
%O A279394 1,3
%A A279394 _Wolfdieter Lang_, Jan 07 2017