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A385454

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

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]

PROG

(Python)

from sympy import divisors

def A385454(n):

l = len(d:=divisors(n))

return n+1-d[l-1>>1]-d[l>>1] # Chai Wah Wu, Jul 01 2025

CROSSREFS

Cf. A063655.

Sequence in context: A274441 A213859 A330492 * A350534 A101336 A300001

Adjacent sequences: A385451 A385452 A385453 * A385455 A385456 A385457