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A226182
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a(n) is the smallest integer k >= 2 such that the number of divisors d>1 of n + k with k|n + d equals A225867(n).
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2
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2, 2, 2, 3, 2, 2, 4, 2, 2, 3, 2, 3, 2, 2, 4, 3, 2, 2, 3, 5, 2, 3, 2, 3, 2, 2, 4, 3, 2, 5, 4, 3, 2, 3, 2, 3, 2, 2, 4, 3, 2, 2, 2, 7, 2, 3, 2, 2, 2, 5, 4, 3, 2, 4, 4, 2, 2, 3, 2, 5, 6, 3, 4, 3, 2, 4, 8, 2, 2, 5, 4, 7, 2, 2, 4, 3, 2, 2, 4, 5, 2, 3, 2, 2, 6, 7, 4
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OFFSET
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6,1
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LINKS
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EXAMPLE
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Let n = 33. We begin with k = 2. Divisors>1 of 33 + 2 = 35 are d = 5,7,35. For all d, 33 + d is divisible by k = 2. But the number of such d is 3, while A225867(33)= 6. Therefore, a(33) > 2. Consider now k = 3. Divisors>1 of 33 + 3 = 36 are 2,3,4,6,9,12,18,36, but only for d = 3,6,9,12,18,36, 33 + d is divisible by k = 3. Since we have exactly A225867(33) = 6 such divisors, then k = 3 is required and a(33) = 3.
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MAPLE
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local ak, k, nd, kpiv ;
ak := 0 ;
kpiv := 2 ;
for k from 2 to n/2-1 do
nd := 0 ;
for d in numtheory[divisors](n+k) minus {1} do
if modp(n+d, k) = 0 then
nd := nd+1;
end if;
end do:
if nd > ak then
ak := max(ak, nd) ;
kpiv := k ;
end if;
end do:
kpiv ;
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MATHEMATICA
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Table[NestWhile[#+1&, 2, Max[Map[Count[(n+Rest[Divisors[n+#]])/#, _Integer]&, Range[2, Floor[(n-2)/2]]]]-Count[(n+Rest[Divisors[n+#]])/#, _Integer] =!= 0&], {n, 6, 55}] (* Peter J. C. Moses, Jun 03 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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STATUS
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approved
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