A384428 a(n) is the minimal area of a polyomino without holes having a product of edge lengths equal to n, or 0 if no solution is possible.

1, 0, 4, 2, 7, 0, 10, 5, 3, 0, 16, 4, 19, 0, 6, 4, 25, 0, 28, 6, 9, 0, 34, 5, 5, 0, 6, 9, 43, 0, 46, 6, 15, 0, 8, 5, 55, 0, 18, 6, 61, 0, 64, 15, 8, 0, 70, 6, 7, 0

Offset: 1

Author

Gordon Hamilton, May 28 2025

Keywords

• nonn
• more

Comments

Good sequence for elementary school students learning multiplication.

If p is the largest prime factor dividing n, then a(n) >= p because there needs to be at least one edge of length k*p for some k>=1.

a(51) > 21. - Sean A. Irvine, Jun 13 2025

Examples

			a(36)=5 because the V pentomino is the smallest polyomino whose edges multiply together to give 36. The edges of the V pentomino are: 3,3,2,2,1,1.
   XXX
   X
   X
a(45)=8 because of the following polyomino with edges 5,3,3,1,1,1,1,1.
   XXXXX
   XX
   X
		

Links

• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A000104, A027709.

Formula

a(4*n+2) = 0.

a(p) = p + (p-1)/2 for any odd prime p.

a(p^2) = p for any prime p.

Extensions

a(33)-a(50) from Sean A. Irvine, Jun 13 2025