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

1,3

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

Links

Table of n, a(n) for n=1..50.

Sean A. Irvine, Java program (github)

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.

Example

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

Crossrefs

Cf. A000104, A027709.

Sequence in context: A155829 A181051 A299631 * A205143 A266394 A353575

Adjacent sequences: A384425 A384426 A384427 * A384429 A384430 A384431

Keyword

nonn,more

Author

Gordon Hamilton, May 28 2025

Extensions

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

Status

approved