

A220114


Largest k >= 0 such that k = n  x  y where n = x*y, x > 0, y > 0, or 1 if no such k exists.


1



1, 1, 1, 0, 1, 1, 1, 2, 3, 3, 1, 5, 1, 5, 7, 8, 1, 9, 1, 11, 11, 9, 1, 14, 15, 11, 15, 17, 1, 19, 1, 20, 19, 15, 23, 24, 1, 17, 23, 27, 1, 29, 1, 29, 31, 21, 1, 34, 35, 35, 31, 35, 1, 39, 39, 41, 35, 27, 1, 44, 1, 29, 47, 48, 47, 49, 1, 47, 43, 53, 1, 55, 1, 35, 55, 53, 59, 59, 1, 62
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OFFSET

1,8


COMMENTS

Any number n can be written as n=1*n, therefore max{ nxy; x>0, y>0, x*y=n } >= 1, with equality for prime numbers.  M. F. Hasler, Dec 29 2012


LINKS

Table of n, a(n) for n=1..80.


FORMULA

a(n) = n  A063655(n).
a(n) = max { nxy ; x>0, y>0, x*y = n }.  M. F. Hasler, Dec 29 2012


EXAMPLE

a(4) = 0 because 4 = 2*2 and 0 = 4  2  2.


MAPLE

A220114 := proc(n)
local k, x;
k := {1} ;
for x in numtheory[divisors](n) do
k := k union {nxn/x} ;
end do:
return max(op(k)) ;
end proc: # R. J. Mathar, Jan 08 2013


CROSSREFS

Sequence in context: A077941 A077990 A085667 * A035516 A120428 A079950
Adjacent sequences: A220111 A220112 A220113 * A220115 A220116 A220117


KEYWORD

sign


AUTHOR

Gerasimov Sergey, Dec 06 2012


EXTENSIONS

Corrected by R. J. Mathar, Jan 08 2013


STATUS

approved



