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A343879
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Number of pairs (d1, d2) of divisors of n such that d1<d2, d1|n, d2|n, d1|d2 and d1 + d2 <= n.
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0
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0, 0, 0, 1, 0, 2, 0, 3, 1, 2, 0, 7, 0, 2, 2, 6, 0, 7, 0, 7, 2, 2, 0, 15, 1, 2, 3, 7, 0, 12, 0, 10, 2, 2, 2, 19, 0, 2, 2, 15, 0, 12, 0, 7, 7, 2, 0, 26, 1, 7, 2, 7, 0, 15, 2, 15, 2, 2, 0, 31, 0, 2, 7, 15, 2, 12, 0, 7, 2, 12, 0, 37, 0, 2, 7, 7, 2, 12, 0, 26, 6, 2, 0, 31, 2, 2, 2, 15
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OFFSET
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1,6
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COMMENTS
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a(n) = 0 if and only if n is noncomposite.
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LINKS
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FORMULA
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a(n) = Sum_{k=1..floor(n/2)} Sum_{i=1..k-1} c(k/i) * c(n/k) * c(n/i), where c(n) = 1 - ceiling(n) + floor(n).
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EXAMPLE
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a(12) = 7; The 7 pairs are (1,2), (1,3), (1,4), (1,6), (2,4), (2,6), (3,6).
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MATHEMATICA
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Table[Sum[Sum[(1 - Ceiling[k/i] + Floor[k/i]) (1 - Ceiling[n/k] + Floor[n/k]) (1 - Ceiling[n/i] + Floor[n/i]), {i, k - 1}], {k, Floor[n/2]}], {n, 100}]
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PROG
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(PARI) a(n) = sumdiv(n, d1, sumdiv(n, d2, if ((d1 < d2) && (d1+d2 <= n) && !(d2 % d1), 1))); \\ Michel Marcus, May 02 2021
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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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