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, 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

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 * A334362 A035516 A120428

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