A035116 -id:A035116 - cp's OEIS frontend

A330571 Square of number of unordered factorizations of n as n = i*j.

1, 1, 1, 4, 1, 4, 1, 4, 4, 4, 1, 9, 1, 4, 4, 9, 1, 9, 1, 9, 4, 4, 1, 16, 4, 4, 4, 9, 1, 16, 1, 9, 4, 4, 4, 25, 1, 4, 4, 16, 1, 16, 1, 9, 9, 4, 1, 25, 4, 9, 4, 9, 1, 16, 4, 16, 4, 4, 1, 36, 1, 4, 9, 16, 4, 16, 1, 9, 4, 16, 1, 36, 1, 4, 9, 9, 4, 16, 1, 25, 9, 4, 1, 36, 4, 4, 4, 16, 1, 36, 4, 9, 4, 4, 4, 36

Offset: 1

N. J. A. Sloane, Jan 08 2020

nonn

Unordered analog of A035116.

For background references see A330570.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Equals A038548(n)^2.

Cf. A035116.

a[n_] := Ceiling[DivisorSigma[0, n] / 2]^2; Array[a, 100] (* Amiram Eldar, Apr 19 2024 *)

a(n) = (numdiv(n) \/ 2)^2; \\ Amiram Eldar, Apr 19 2024

A130277 Triangle read by rows: A130209 * A051731 as infinite lower triangular matrices.

Original entry on oeis.org

1, 2, 2, 2, 0, 2, 3, 3, 0, 3, 2, 0, 0, 0, 2, 4, 4, 4, 0, 0, 4, 2, 0, 0, 0, 0, 0, 2, 4, 4, 0, 4, 0, 0, 0, 4, 3, 0, 3, 0, 0, 0, 0, 0, 3, 4, 4, 0, 0, 4, 0, 0, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 6, 6, 6, 0, 6, 0, 0, 0, 0, 0, 6, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4

Offset: 1

Gary W. Adamson, May 18 2007

Row sums = A035116: (1, 4, 4, 9, 4, 16, 4, 16, ...).

Right and left borders = A000005, d(n): (1, 2, 2, 3, 2, 4, 2, ...).

			First few rows of the triangle:
  1;
  2, 2;
  2, 0, 2;
  3, 3, 0, 3;
  2, 0, 0, 0, 2;
  4, 4, 4, 0, 0, 4;
  2, 0, 0, 0, 0, 0, 2;
  4, 4, 0, 4, 0, 0, 0, 4;
  ...

Cf. A000005, A035116, A051731, A130209.

a(56) corrected and more terms from Georg Fischer, Jun 05 2023

cp's OEIS Frontend

A330571 Square of number of unordered factorizations of n as n = i*j.

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