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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

Any number n can be written as n=1*n, therefore max{ n-x-y; 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 { n-x-y ; 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 {n-x-n/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

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Last modified February 20 02:07 EST 2018. Contains 299357 sequences. (Running on oeis4.)