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

0,1

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).

Formula

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

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 *)

Prog

(Haskell)
a242627 n = length $ filter ((== 0) . mod n) [1..9]
(PARI) a(n)=1+sum(k=2, 9, n%k<1) \\ Zak Seidov, Jul 31 2014

Crossrefs

Cf. A165412.

Sequence in context: A354347 A010166 A186116 * A289502 A010165 A177273

Adjacent sequences: A242624 A242625 A242626 * A242628 A242629 A242630

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jul 16 2014

Status

approved