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).

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, 50, 126, 257, 244, 65, 1, 2, 9, 50, 252, 626, 1025, 730, 129, 1, 4, 10, 65, 344, 1394, 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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..77.

Eric Weisstein's World of Mathematics, Unitary Divisor

Eric Weisstein's World of Mathematics, Unitary Divisor Function

Index entries for sequences related to sums of divisors

Formula

Dirichlet g.f. of row n: zeta(s)*zeta(s-n)/zeta(2*s-n).

Example

Square array begins:
1,   2,    2,     2,     2,     4,  ...
1,   3,    4,     5,     6,    12,  ...
1,   5,   10,    17,    26,    50,  ...
1,   9,   28,    65,   126,   252,  ...
1,  17,   82,   257,   626,  1394,  ...
1,  33,  244,  1025,  3126,  8052,  ...

Crossrefs

Rows n=0-8 give: A034444, A034448, A034676, A034677, A034678, A034679, A034680, A034681, A034682.

Cf. A077610, A109974, A285425.

Sequence in context: A263744 A268956 A208515 * A178030 A131879 A172288

Adjacent sequences: A286877 A286878 A286879 * A286881 A286882 A286883

Keyword

nonn,tabl

Author

Ilya Gutkovskiy, Aug 02 2017

Status

approved