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%I #13 May 20 2021 08:57:27
%S 1,2,1,2,3,1,2,4,5,1,2,5,10,9,1,4,6,17,28,17,1,2,12,26,65,82,33,1,2,8,
%T 50,126,257,244,65,1,2,9,50,252,626,1025,730,129,1,4,10,65,344,1394,
%U 3126,4097,2188,257,1,2,18,82,513,2402,8052,15626,16385,6562,513,1,4,12,130,730,4097,16808,47450,78126,65537,19684,1025,1
%N Square array A(n,k), n>=0, k>=1, read by antidiagonals, where row n is the sum of n-th powers of unitary divisors of k (divisors d such that gcd(d, k/d) = 1).
%C For row r > 0, Sum_{k=1..n} A(r,k) ~ zeta(r+1) * n^(r+1) / ((r+1) * zeta(r+2)). - _Vaclav Kotesovec_, May 20 2021
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitaryDivisor.html">Unitary Divisor</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnitaryDivisorFunction.html">Unitary Divisor Function</a>
%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F Dirichlet g.f. of row n: zeta(s)*zeta(s-n)/zeta(2*s-n).
%e Square array begins:
%e 1, 2, 2, 2, 2, 4, ...
%e 1, 3, 4, 5, 6, 12, ...
%e 1, 5, 10, 17, 26, 50, ...
%e 1, 9, 28, 65, 126, 252, ...
%e 1, 17, 82, 257, 626, 1394, ...
%e 1, 33, 244, 1025, 3126, 8052, ...
%Y Rows n=0-8 give: A034444, A034448, A034676, A034677, A034678, A034679, A034680, A034681, A034682.
%Y Cf. A077610, A109974, A285425.
%K nonn,tabl
%O 0,2
%A _Ilya Gutkovskiy_, Aug 02 2017
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