A083230 - OEIS

%I #25 Sep 27 2023 13:37:37

%S 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,

%T 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,

%U 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

%N Number of repunit divisors of n.

%C Differs from A043284 (maximal run length in decimal expansion) from a(100) on. - _M. F. Hasler_, Oct 18 2019

%H Paolo Xausa, <a href="/A083230/b083230.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1221 from Andrew Howroyd)

%e n = 110, divisors are {1, 2, 5, 10, 11, 22, 55, 110} with two repunits: 1 and 11, therefore a(110) = 2.

%e n = 111, divisors are {1, 3, 37, 111} with two repunits: 1 and 111, therefore a(111) = 2.

%e 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.

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

%o (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

%Y Cf. A000005, A002275, A043284.

%Y Cf. A109492.

%K nonn,base

%O 1,11

%A _Reinhard Zumkeller_, Jun 01 2003