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A286880 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).

%I A286880 #14 Feb 16 2025 08:33:45
%S A286880 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 A286880 50,126,257,244,65,1,2,9,50,252,626,1025,730,129,1,4,10,65,344,1394,
%U A286880 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 A286880 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 A286880 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 A286880 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnitaryDivisor.html">Unitary Divisor</a>
%H A286880 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnitaryDivisorFunction.html">Unitary Divisor Function</a>
%H A286880 <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F A286880 Dirichlet g.f. of row n: zeta(s)*zeta(s-n)/zeta(2*s-n).
%e A286880 Square array begins:
%e A286880 1,   2,    2,     2,     2,     4,  ...
%e A286880 1,   3,    4,     5,     6,    12,  ...
%e A286880 1,   5,   10,    17,    26,    50,  ...
%e A286880 1,   9,   28,    65,   126,   252,  ...
%e A286880 1,  17,   82,   257,   626,  1394,  ...
%e A286880 1,  33,  244,  1025,  3126,  8052,  ...
%Y A286880 Rows n=0-8 give: A034444, A034448, A034676, A034677, A034678, A034679, A034680, A034681, A034682.
%Y A286880 Cf. A077610, A109974, A285425.
%K A286880 nonn,tabl
%O A286880 0,2
%A A286880 _Ilya Gutkovskiy_, Aug 02 2017