A083230 Number of repunit divisors of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Reinhard Zumkeller, Jun 01 2003

Keywords

• nonn
• base

Comments

Differs from A043284 (maximal run length in decimal expansion) from a(100) on. - M. F. Hasler, Oct 18 2019

Examples

			n = 110, divisors are {1, 2, 5, 10, 11, 22, 55, 110} with two repunits: 1 and 11, therefore a(110) = 2.
n = 111, divisors are {1, 3, 37, 111} with two repunits: 1 and 111, therefore a(111) = 2.
n = 111111, divisors are {1, 3, 7, 11, 13, 21, 33, 37, 39, 77, 91, 111, 143, 231, 259, 273, 407, 429, 481, 777, 1001, 1221, 1443, 2849, 3003, 3367, 5291, 8547, 10101, 15873, 37037, 111111} with four repunits: 1, 11, 111 and 111111, therefore a(111111) = 4.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000 (terms 1..1221 from Andrew Howroyd)

Crossrefs

Cf. A000005, A002275, A043284, A065444.

Cf. A109492.

Programs

Mathematica

A083230[n_]:=Count[IntegerDigits[Divisors[n]],{1..}];Array[A083230,100] (* Paolo Xausa, Sep 27 2023 *)

PARI

a(n)={my(s=0, k=1); while(k<=n, if(n%k==0, s++); k=10*k+1); s} \\ Andrew Howroyd, Aug 07 2018

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A065444. - Amiram Eldar, Apr 17 2025