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A178776
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a(n) is the largest number that appears twice in an n x n multiplication table of positive integers, disregarding the pairs that are obviously produced by the commutative property.
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0
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4, 4, 12, 12, 24, 36, 40, 40, 72, 72, 84, 120, 144, 144, 180, 180, 240, 252, 252, 252, 360, 400, 400, 432, 504, 504, 600, 600, 672, 672, 672, 840, 900, 900, 900, 936, 1120, 1120, 1260, 1260, 1320, 1440, 1440, 1440, 1680, 1764, 1800, 1800, 1872, 1872
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OFFSET
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4,1
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COMMENTS
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It appears that all terms of this sequence are multiple of 4 (checked up to 10^7). - Michel Marcus, Aug 26 2013
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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