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A136529
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a(n) = the smallest possible number of positive divisors of the sum of any two distinct positive divisors of n.
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2
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2, 3, 2, 4, 2, 4, 2, 3, 2, 6, 2, 4, 2, 3, 2, 6, 2, 6, 2, 3, 2, 8, 2, 4, 2, 3, 2, 8, 2, 6, 2, 3, 2, 4, 2, 4, 2, 3, 2, 8, 2, 6, 2, 3, 2, 10, 2, 4, 2, 3, 2, 8, 2, 4, 2, 3, 2, 12, 2, 4, 2, 3, 2, 4, 2, 6, 2, 3, 2, 12, 2, 4, 2, 3, 2, 4, 2, 10, 2, 3, 2, 12, 2, 4, 2, 3, 2, 12, 2, 4, 2, 3, 2, 4, 2, 6, 2, 3, 2, 8, 2, 8
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OFFSET
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2,1
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COMMENTS
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There are d(n)*(d(n)-1)/2 sums of pairs of distinct positive divisors of n, where d(n) = number of positive divisors of n.
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LINKS
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EXAMPLE
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The positive divisors of 6 are 1,2,3,6. Letting d(m) = the number of positive divisors of m: d(1+2)=2; d(1+3)=3; d(1+6)=2; d(2+3)=2; d(2+6)=4; d(3+6)=3. The least of these values is 2, so a(6) = 2.
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PROG
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(PARI) { a(n) = d=divisors(n); m=numdiv(n+1); for(i=1, #d, for(j=i+1, #d, m=min(m, numdiv(d[i]+d[j])); )); m } \\ Max Alekseyev, Apr 27 2009
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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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