A243162 Numbers n such that n^2 divides n.n.n where dot "." means concatenation.

1, 3, 13, 21, 37, 39, 91, 1443, 3367, 9901, 157737, 333667, 999001, 3075403, 9226209, 14287143, 33336667, 99990001, 1171182883, 1224848037, 1286294191, 1397863441, 1428557143, 1469179621, 1535254357, 1568996211, 1753536967, 1792076241, 1839599913, 1891910811

Offset

1,2

Comments

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.

Numbers n such that n divides 100^d+10^d+1, where 10^(d-1)<=n<10^d. - Robert Israel, Jan 11 2017

Links

Hans Havermann, Table of n, a(n) for n = 1..1366

Example

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

Maple

Res:= {}:
for d from 1 to 15 do
  Res:= Res union select(t -> t >= 10^(d-1) and t < 10^d,
   numtheory:-divisors(100^d+10^d+1))
od:
sort(convert(Res, list)); # Robert Israel, Jan 11 2017

Mathematica

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}]

Crossrefs

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

Contains A074992 and A168624.

Sequence in context: A055059 A050903 A117766 * A147351 A147097 A147105

Adjacent sequences: A243159 A243160 A243161 * A243163 A243164 A243165

Keyword

nonn,base

Author

Hans Havermann, May 31 2014

Status

approved