A330572 a(n) = Sum_{k = 1..n} [u_2(k)*u_2(n+1-k)], where u_2(k) is the number of unordered factorizations k = i*j (A038548).

0, 1, 2, 3, 6, 7, 10, 12, 14, 19, 20, 24, 28, 31, 32, 40, 40, 48, 48, 56, 56, 67, 60, 77, 72, 85, 80, 98, 88, 108, 98, 117, 110, 131, 110, 147, 128, 149, 140, 169, 144, 182, 154, 192, 174, 205, 168, 228, 188, 226, 208, 250, 204, 268, 218, 273, 246, 285, 234, 324

Offset: 0

Author

N. J. A. Sloane, Jan 08 2020

Keywords

• nonn
• look

Comments

An analog of A055507 for unordered factorizations.

For background references see A330570.

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000005, A038548, A055507.

See A330573 for another version.

Programs

Maple

u2:= proc(n) option remember; if issqr(n) then (numtheory:-tau(n)+1)/2 else numtheory:-tau(n)/2 fi end proc:
f:= proc(n) local k; add(u2(k)*u2(n+1-k),k=1..n) end proc:
map(f, [$0..100]); # Robert Israel, Dec 05 2022

Mathematica

s[n_] := s[n] = Ceiling[DivisorSigma[0, n] / 2]; a[n_] := Sum[s[k] * s[n+1-k], {k, 1, n}]; Array[a, 100, 0] (* Amiram Eldar, Apr 19 2024 *)

Extensions

Offset corrected by Robert Israel, Dec 05 2022