A225299 Numbers divisible by the square of each digit.

1, 11, 12, 36, 111, 112, 128, 144, 212, 216, 224, 333, 432, 448, 612, 1111, 1112, 1116, 1212, 1296, 1332, 1424, 2112, 2144, 2212, 2224, 2232, 2916, 3132, 3312, 3636, 4112, 4144, 4224, 4288, 4464, 6336, 6624, 8128, 8448, 9396, 11111, 11112, 11133, 11172, 11212

Offset

1,2

Comments

Includes all repunits.

Links

Christian N. K. Anderson, Table of n, a(n) for n = 1..5000

Example

a(7) 128 is divisible by 1^2, by 2^2, and by 8^2.

Mathematica

d[n_]:=IntegerDigits[n]; t={}; Do[If[!MemberQ[d[n], 0] && Union[Mod[n, d[n]^2]] == {0}, AppendTo[t, n]], {n, 11220}]; t (* Jayanta Basu, May 15 2013 *)
Select[Range[12000], DigitCount[#, 10, 0]==0&&And@@Divisible[ #, IntegerDigits[ #]^2]&] (* Harvey P. Dale, Jul 16 2018 *)

Prog

(R) isint<-function(x) x==as.integer(x)
sqalldig<-function(x) as.numeric(strsplit(as.character(x), "")[[1]])^2
divby<-function(x) ifelse(length(grep(0, x))>0, F, all(isint(x/sqalldig(x))))
which(sapply(1:1000, divby))

Crossrefs

Cf. A132359, A034709, A034837, A005349, A007602, A034838.

Sequence in context: A244068 A041252 A041250 * A290336 A300405 A248323

Adjacent sequences: A225296 A225297 A225298 * A225300 A225301 A225302

Keyword

nonn,base

Author

Kevin L. Schwartz and Christian N. K. Anderson, May 04 2013

Status

approved