A082477 Number of divisors d of n such that d+1 is also a divisor of n+1.

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

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

Adjacent sequences: A082474 A082475 A082476 * A082478 A082479 A082480

Keyword

nonn

Author

Benoit Cloitre, Apr 27 2003

Status

approved