A394362 Number of divisors d of n which also divide n/d + 1.

1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 4, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 3, 1, 1, 2, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 3, 2, 2, 1, 2, 2, 2, 1, 2, 1, 1

Offset

1,2

Links

James C. McMahon, Table of n, a(n) for n = 1..10000

Example

a(2) = 2 because 2/d + 1 == 0 (mod d) for d = 1 (or 2) of n = 2;
a(6) = 3 because 6/d + 1 == 0 (mod d) for d = 1 (or 2, 3) of n = 6, but d = 6 is a nondivisor of 2 = 6/6 + 1.

Maple

a:= n-> add(`if`(irem(n/d+1, d)=0, 1, 0), d=numtheory[divisors](n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 20 2026

Mathematica

fmod[n_, d_]:=Mod[n/d+1, d]; a[n_]:=Module[{d=Divisors[n]}, Count[fmod[n, d], 0]]; Array[a, 100] (* James C. McMahon, Mar 28 2026 *)

Prog

(Magma) [#[d: d in Divisors(n) | ((n div d) + 1) mod d eq 0]: n in [1..100]];

Crossrefs

Cf. A000005, A014567, A046951, A069059, A163671 (number of divisors d of n which also divide n/d - 1).

Sequence in context: A224765 A369167 A160267 * A115621 A326514 A077565

Adjacent sequences: A394359 A394360 A394361 * A394363 A394364 A394365

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 18 2026

Status

approved