A242627 - OEIS

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

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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