A163520 a(n) is the least integer x such that n < x and the product n*x is divisible by an integer y where n < y < x.

4, 6, 8, 9, 12, 12, 16, 15, 16, 18, 24, 20, 28, 24, 24, 25, 36, 28, 40, 30, 32, 36, 48, 35, 36, 42, 40, 40, 60, 42, 64, 45, 48, 54, 48, 49, 76, 60, 56, 54, 84, 56, 88, 60, 60, 72, 96, 63, 64, 66, 72, 70, 108, 70, 72, 72, 80, 90, 120, 77, 124, 96, 80, 81

Offset

1,1

Comments

a(n) is the smallest area of an integer-sided rectangle able to enclose without contact an integer-sided rectangle of area n. The enclosing rectangle has sides A033676(n)+1 and A033677(n)+1. See the first formula below. - Peter Munn, Apr 26 2019

Links

Table of n, a(n) for n=1..64.

Estonian Math Competitions 2008/2009, problem TS-6, pages 23-24

Formula

a(n) = (A033676(n)+1) * (A033677(n)+1).

a(n) = n + A033676(n) + A033677(n) + 1.

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

a(n^2) = (n+1)^2; a(n^2-n) = n^2 + n.

a(p) = 2*(p+1) for p prime.

Example

For example, a(6)=12
since 6*7 is not divisible by any number between 6 and 7,
and 6*8 is not divisible by any number between 6 and 8,
and 6*9 is not divisible by any number between 6 and 9,
and 6*10 is not divisible by any number between 6 and 10,
and 6*11 is not divisible by any number between 6 and 11,
but 6*12 is divisible by 9 which is between 6 and 12.

Crossrefs

Cf. A033676, A033677, A063655.

Sequence in context: A084985 A068631 A338461 * A273546 A176539 A285256

Adjacent sequences: A163517 A163518 A163519 * A163521 A163522 A163523

Keyword

nonn

Author

Harmel Nestra (harmel.nestra(AT)ut.ee), Jul 30 2009

Extensions

Formulas extended by Franklin T. Adams-Watters, Aug 06 2009

Status

approved