cp's OEIS Frontend

A083230 Number of repunit divisors of n.

%I A083230 #29 Apr 17 2025 08:09:09
%S A083230 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 A083230 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 A083230 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 A083230 Number of repunit divisors of n.
%C A083230 Differs from A043284 (maximal run length in decimal expansion) from a(100) on. - _M. F. Hasler_, Oct 18 2019
%H A083230 Paolo Xausa, <a href="/A083230/b083230.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1221 from Andrew Howroyd)
%F A083230 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = A065444. - _Amiram Eldar_, Apr 17 2025
%e A083230 n = 110, divisors are {1, 2, 5, 10, 11, 22, 55, 110} with two repunits: 1 and 11, therefore a(110) = 2.
%e A083230 n = 111, divisors are {1, 3, 37, 111} with two repunits: 1 and 111, therefore a(111) = 2.
%e A083230 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 A083230[n_]:=Count[IntegerDigits[Divisors[n]],{1..}];Array[A083230,100] (* _Paolo Xausa_, Sep 27 2023 *)
%o A083230 (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 A083230 Cf. A000005, A002275, A043284, A065444.
%Y A083230 Cf. A109492.
%K A083230 nonn,base
%O A083230 1,11
%A A083230 _Reinhard Zumkeller_, Jun 01 2003