A243162 - OEIS

%I #14 Jan 12 2017 06:33:46

%S 1,3,13,21,37,39,91,1443,3367,9901,157737,333667,999001,3075403,

%T 9226209,14287143,33336667,99990001,1171182883,1224848037,1286294191,

%U 1397863441,1428557143,1469179621,1535254357,1568996211,1753536967,1792076241,1839599913,1891910811

%N Numbers n such that n^2 divides n.n.n where dot "." means concatenation.

%C Number of d-digit solutions for d = 1..100: 2, 5, 0, 3, 0, 3, 2, 3, 0, 39, 0, 2, 0, 106, 0, 3, 3, 2, 0, 441, 4, 14, 0, 5, 0, 15, 2, 283, 0, 23, 0, 61, 0, 24, 21, 4, 0, 22, 0, 240, 0, 34, 0, 96, 3, 30, 0, 6, 16, 281, 0, 216, 0, 22, 5, 3894, 2, 10, 0, 149, 2, 11, 0, 407, 0, 25, 0, 2136, 0, 53983, 0, 12, 1, 29, 11, 1872, 99, 20, 0, 6984, 0, 45, 0, 279, 32, 10, 5, 15928, 0, 213, 24, 791, 0, 20, 14, 44, 0, 713, 12, 89804.

%C Numbers n such that n divides 100^d+10^d+1, where 10^(d-1)<=n<10^d. - _Robert Israel_, Jan 11 2017

%H Hans Havermann, <a href="/A243162/b243162.txt">Table of n, a(n) for n = 1..1366</a>

%e 21^2 divides 212121; 91^2 divides 919191; so both 21 and 91 are in the sequence.

%p Res:= {}:

%p for d from 1 to 15 do

%p   Res:= Res union select(t -> t >= 10^(d-1) and t < 10^d,

%p    numtheory:-divisors(100^d+10^d+1))

%p od:

%p sort(convert(Res,list)); # _Robert Israel_, Jan 11 2017

%t Do[d=Divisors[100^i+10^i+1];s=Select[d,Length[IntegerDigits[#]]==i&];If[Length[s]>0,Do[Print[s[[j]]],{j,Length[s]}]],{i,42}]

%Y Cf. A147553 (n^2 divides n.n), A147554 (primes in this sequence).

%Y Contains A074992 and A168624.

%K nonn,base

%O 1,2

%A _Hans Havermann_, May 31 2014