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A308477 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{j=1..n, gcd(n,j) = 1} j^k.

%I A308477 #10 May 30 2019 11:52:03
%S A308477 1,1,1,1,1,2,1,1,3,2,1,1,5,4,4,1,1,9,10,10,2,1,1,17,28,30,6,6,1,1,33,
%T A308477 82,100,26,21,4,1,1,65,244,354,126,91,16,6,1,1,129,730,1300,626,441,
%U A308477 84,27,4,1,1,257,2188,4890,3126,2275,496,159,20,10,1,1,513,6562,18700,15626,12201,3108,1053,140,55,4
%N A308477 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals: A(n,k) = Sum_{j=1..n, gcd(n,j) = 1} j^k.
%H A308477 Seiichi Manyama, <a href="/A308477/b308477.txt">Antidiagonals n = 1..140, flattened</a>
%e A308477 Square array begins:
%e A308477   1,   1,   1,    1,    1,     1,  ...
%e A308477   1,   1,   1,    1,    1,     1,  ...
%e A308477   2,   3,   5,    9,   17,    33,  ...
%e A308477   2,   4,  10,   28,   82,   244,  ...
%e A308477   4,  10,  30,  100,  354,  1300,  ...
%e A308477   2,   6,  26,  126,  626,  3126,  ...
%t A308477 Table[Function[k, Sum[If[GCD[n, j] == 1, j^k, 0], {j, 1, n}]][i - n], {i, 0, 12}, {n, 1, i}] // Flatten
%Y A308477 Columns k=0..4 give A000010, A023896, A053818, A053819, A053820.
%Y A308477 Cf. A103438.
%K A308477 nonn,tabl
%O A308477 1,6
%A A308477 _Ilya Gutkovskiy_, May 29 2019