

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.


0



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
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OFFSET

1,1


COMMENTS

a(n) is the smallest area of an integersided rectangle able to enclose without contact an integersided 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 TS6, pages 2324


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^2n) = 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: A202268 A084985 A068631 * 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. AdamsWatters, Aug 06 2009


STATUS

approved



