OFFSET
4,1
COMMENTS
It appears that all terms of this sequence are multiple of 4 (checked up to 10^7). - Michel Marcus, Aug 26 2013
FORMULA
Let xy = n be the factorization of n such that x+y is a minimum. We then have a(4)= 4 and a(n)= max{a(n-1), xy(x-1)(y-1)} for all n>4.
EXAMPLE
The first term is 4, which appears twice in a 4 x 4 multiplication table. a(4) = 2x2 = 4x1 = 4. For all n = prime a(n) = a(n-1) so a(5) = 4. a(6) = 12 = 2x6 = 3x4, a(7) = 12, a(8) = 24 = 3x8 = 4x6, a(9) = 36 = 4x9 = 6x6.
PROG
(PARI) a(n) = {skeep = Set(); mmax = 0; for (i = 1, n, for (j = i, n, v = i*j; if (! setsearch(skeep, v), skeep = setunion(skeep, Set(v)), mmax = max(mmax, v)); ); ); mmax; } \\ Michel Marcus, Aug 26 2013
(PARI) findxy(n, d) = {mins = 2*n; if (#d % 2, nd = #d\2 +1, nd = #d/2); for (i = 1, nd, if ((s = d[i]+n/d[i]) < mins, mins = s; mini = i); ); x = d[mini]; y = n/x; return (x*y*(x-1)*(y-1)); }
lista(nn) = {lmmx = 4; print1(lmmx, ", "); for (n=5, nn, d = divisors(n); nmmx = findxy(n, d); lmmx = max(lmmx, nmmx); print1(lmmx, ", "); ); } \\ Michel Marcus, Aug 26 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary Yane, Jun 11 2010
EXTENSIONS
Edited by N. J. A. Sloane, Jun 12 2010
Corrected by Michel Marcus, Aug 26 2013
STATUS
approved