A242627 Number of divisors of n that are less than 10.

9, 1, 2, 2, 3, 2, 4, 2, 4, 3, 3, 1, 5, 1, 3, 3, 4, 1, 5, 1, 4, 3, 2, 1, 6, 2, 2, 3, 4, 1, 5, 1, 4, 2, 2, 3, 6, 1, 2, 2, 5, 1, 5, 1, 3, 4, 2, 1, 6, 2, 3, 2, 3, 1, 5, 2, 5, 2, 2, 1, 6, 1, 2, 4, 4, 2, 4, 1, 3, 2, 4, 1, 7, 1, 2, 3, 3, 2, 4, 1, 5, 3, 2, 1, 6, 2

Offset: 0

Author

Reinhard Zumkeller, Jul 16 2014

Keywords

• nonn
• easy

Comments

Number of numbers <= 9, dividing n;

a(n) <= 9; a(2520*n) = 9;

a(n) = (number of repdigit numbers in row n of triangle A242614) = sum(A202022(A242614(n,k)): k=1..A242622(n)), for n > 0.

Periodic with period 2520. Each period there are 576 1's, 720 2's, 464 3's, 360 4's, 206 5's, 122 6's, 58 7's, 13 8's, and 1 9 (average 2.82...). - Charles R Greathouse IV, Sep 27 2015

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (-2,-4,-7,-11,-15,-20,-24,-27,-28,-27,-23,-17,-9,0,9,17,23,27,28,27,24,20,15,11,7,4,2,1).

Crossrefs

Cf. A165412.

Programs

Haskell

a242627 n = length $ filter ((== 0) . mod n) [1..9]

Maple

a:= n -> numboccur(0,map2(`modp`,n,[$1..9])):
map(a,[$0..100]); # Robert Israel, Jul 31 2014

Mathematica

a[n_] := If[n == 0, 9, Count[Divisors[n], d_ /; d < 10]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Dec 13 2021 *)

PARI

a(n)=1+sum(k=2,9,n%k<1) \\ Zak Seidov, Jul 31 2014

Formula

G.f.: Sum_(j=1..9, 1/(1-x^j)). - Robert Israel, Jul 31 2014