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A082477
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Number of divisors d of n such that d+1 is also a divisor of n+1.
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2
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1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 3, 1, 2, 1, 2, 3, 2, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 4, 2, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 3, 2, 1, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 1, 3, 1, 2, 2, 4, 1, 2, 1, 2, 3, 2
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OFFSET
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1,3
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COMMENTS
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The partial sums of this sequence from k = 1 to 10^m, for m = 1, 2, ..., are 15, 185, 1952, 19852, 199538, 1998538, 19995362, 199985379, 1999953823, ... . Conjecture: The asymptotic mean of this sequence is 2. - Amiram Eldar, Jun 04 2022
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LINKS
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FORMULA
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MATHEMATICA
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ndd[n_]:=Count[Divisors[n], _?(Divisible[n+1, #+1]&)]; Array[ndd, 110] (* Harvey P. Dale, Aug 29 2015 *)
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PROG
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(PARI) a(n)=sumdiv(n, d, if((n+1)%(d+1), 0, 1))
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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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