A140583 Triangle read by rows: T(n,k) = Sum_{i=k..n} A140581(n,i).

1, 2, 1, 3, 1, 1, 2, 2, 1, 1, 5, 1, 1, 1, 1, 1, 4, 2, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 6, 2, 2, 2, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 2, 2, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Formula

Equals A140581 * A000012 as infinite lower triangular matrices.

Example

First few rows of the triangle:
  1;
  2, 1;
  3, 1, 1;
  2, 2, 1, 1;
  5, 1, 1, 1, 1;
  1, 4, 2, 1, 1, 1;
  7, 1, 1, 1, 1, 1, 1;
  2, 2, 2, 2, 1, 1, 1, 1;
  3, 3, 3, 1, 1, 1, 1, 1, 1;
  1, 6, 2, 2, 2, 1, 1, 1, 1, 1;
  ...

Prog

(PARI) \\ here b(n) is A014963 and U(n, k) is A140581.
b(n)=ispower(n, , &n); if(isprime(n), n, 1)
U(n, k) = if(n%k==0, my(r=n/k); sumdiv(r, d, moebius(d)*b(r/d)), 0)
T(n, k) = sum(i=k, n, U(n, i)) \\ Andrew Howroyd, Sep 20 2025

Crossrefs

Column 1 is A014963.

Row sums are A140584.

Cf. A140581.

Sequence in context: A351094 A351092 A138618 * A237266 A123507 A384009

Adjacent sequences: A140580 A140581 A140582 * A140584 A140585 A140586

Keyword

nonn,tabl

Author

Gary W. Adamson and Mats Granvik, May 17 2008

Extensions

Name edited and a(79) onwards from Andrew Howroyd, Sep 20 2025

Status

approved