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A088722
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Number of divisors d>1 of n such that d+1 also divides n.
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12
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0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 0
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OFFSET
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1,12
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COMMENTS
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Also, number of partitions of n into two distinct parts (s,t), s<t, such that s|n and t|s*n. - Wesley Ivan Hurt, Jan 16 2022
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LINKS
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FORMULA
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Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/2. (End)
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EXAMPLE
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n=144: divisors(144) = {1,2,3,4,6,8,9,12,16,18,24,36,48,72,144}, there are a(144) = 3 divisors d>1 such that also d+1 divides 144: (2,3), (3,4) and (8,9).
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MATHEMATICA
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Table[DivisorSum[n, 1 &, And[# > 1, Divisible[n, # + 1]] &], {n, 105}] (* Michael De Vlieger, Jul 12 2017 *)
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PROG
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(PARI) first(n) = my(v = vector(n), k); for(i=2, sqrtint(n), k=i*(i+1); for(j=1, n\k, v[j*k]++)); v \\ David A. Corneth, Jul 12 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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