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A225299
Numbers divisible by the square of each digit.
2
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
KEYWORD
nonn,base
STATUS
approved