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

Author

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

Keywords

• nonn
• base

Comments

Includes all repunits.

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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))