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A082477
Number of divisors d of n such that d+1 is also a divisor of n+1.
2
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
OFFSET
1,3
COMMENTS
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
LINKS
FORMULA
G.f.: Sum_{k>0} x^k/(1-x^(k*(k+1))). - Vladeta Jovovic, Apr 21 2010
MATHEMATICA
ndd[n_]:=Count[Divisors[n], _?(Divisible[n+1, #+1]&)]; Array[ndd, 110] (* Harvey P. Dale, Aug 29 2015 *)
PROG
(PARI) a(n)=sumdiv(n, d, if((n+1)%(d+1), 0, 1))
CROSSREFS
Cf. A082478.
Sequence in context: A072491 A051034 A024935 * A036430 A323305 A322794
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 27 2003
STATUS
approved