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A195150
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Number of divisors d of n such that d-1 does not divide n.
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3
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0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 3, 3, 1, 3, 1, 3, 3, 2, 1, 4, 2, 2, 3, 4, 1, 4, 1, 4, 3, 2, 3, 5, 1, 2, 3, 5, 1, 4, 1, 4, 5, 2, 1, 6, 2, 4, 3, 4, 1, 5, 3, 5, 3, 2, 1, 6, 1, 2, 5, 5, 3, 5, 1, 4, 3, 6, 1, 7, 1, 2, 5, 4, 3, 5, 1, 7, 4, 2, 1, 7, 3, 2
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OFFSET
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1,8
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COMMENTS
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Define "subdivisor" of n to be the positive integer b such that b = d - 1, if d divides n and b does not divide n. For the list of subdivisors of n see A195153.
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ n * (log(n) + 2*gamma - 3), where gamma is Euler's constant (A001620). - Amiram Eldar, Jan 18 2024
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EXAMPLE
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a(24) = 4 since the divisors of 24 are 1,2,3,4,6,8,12,24, so the subdivisors of 24 are 5,7,11,23 because 6-1 = 5, 8-1 = 7, 12-1 = 11 and 24-1 = 23. Note that the positive integers 1,2,3 are not subdivisors of 24 because they are divisors of 24.
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MATHEMATICA
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f[n_] := Module[{d = Divisors[n]}, Length[Select[Rest[d-1], Mod[n, #] > 0 &]]]; Table[f[n], {n, 100}] (* T. D. Noe, Sep 22 2011 *)
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PROG
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(Haskell)
a195150 n = length [d | d <- [3..n], mod n d == 0, mod n (d-1) /= 0]
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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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STATUS
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approved
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