A385454 - Contribution to The OEIS: Difference of the largest and smallest semiperimeters of an integral rectangle with area n.

 A385454

Difference of the largest and smallest semiperimeters of an integral rectangle with area n.

0

0, 0, 0, 1, 0, 2, 0, 3, 4, 4, 0, 6, 0, 6, 8, 9, 0, 10, 0, 12, 12, 10, 0, 15, 16, 12, 16, 18, 0, 20, 0, 21, 20, 16, 24, 25, 0, 18, 24, 28, 0, 30, 0, 30, 32, 22, 0, 35, 36, 36, 32, 36, 0, 40, 40, 42, 36, 28, 0, 45, 0, 30, 48, 49, 48, 50, 0, 48, 44, 54, 0, 56, 0

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OFFSET

1,6

COMMENTS

For all noncomposite n, a(n) = 0.

For each square k^2, a(k^2) = (k^2 + 1) - 2*k = (k-1)^2.

LINKS

James C. McMahon, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = 1 + n - A063655(n).

EXAMPLE

The largest semiperimeter of an integral rectangle with area 9 is 10 (1 x 9 rectangle); the smallest semiperimeter is 6 (3 x 3 rectangle). The difference, a(9) = 4.

MATHEMATICA

a[n_]:=1+n-2Median[Divisors[n]]; Array[a, 73]

CROSSREFS

Cf. A063655.

Sequence in context: A274441 A213859 A330492 * A350534 A101336 A300001

Adjacent sequences: A385442 A385443 A385444 * A385459 A385460 A385461

KEYWORD

nonn,new

AUTHOR

James C. McMahon, Jun 29 2025

STATUS

approved