A132359 Numbers divisible by the square of their last decimal digit.

1, 11, 12, 21, 25, 31, 32, 36, 41, 51, 52, 61, 63, 64, 71, 72, 75, 81, 91, 92, 101, 111, 112, 121, 125, 128, 131, 132, 141, 144, 147, 151, 152, 153, 161, 171, 172, 175, 181, 191, 192, 201, 211, 212, 216, 221, 224, 225, 231, 232, 241, 243, 251, 252, 261, 271, 272

Offset: 1

Author

Jonathan Vos Post, Nov 08 2007

Keywords

• base
• easy
• nonn
• nice

Comments

Subsequences are A017281 and A053742 representing last digits 1 and 5. Generators for the subsequences representing last digits 2, 3, 4, 6, 7, 8 and 9 are, in that order, the terms 12+20i, 63+90i, 64+80i, 36+180i, 147+490i, 128+320i, 729+810i, where i=0,1,2,... - R. J. Mathar, Nov 13 2007

This is a 10-automatic sequence. - Charles R Greathouse IV, Dec 28 2011

Examples

			147 belongs to the sequence because 147/7^2 = 3.
		

Links

• T. D. Noe and Christian N. K. Anderson, Table of n, a(n) for n = 1..10000 (first 1000 values from T. D. Noe)
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A034709, A225722, A221651, A225296, A225297, A034709, A034837, A005349, A007602, A034838, A225297.

Programs

Maple

isA132359 := proc(n) local ldig ; ldig := n mod 10 ; if ldig <> 0 and n mod (ldig^2) = 0 then true ; else false ; fi ; end: for n from 1 to 400 do if isA132359(n) then printf("%d,",n) ; fi ; od: # R. J. Mathar, Nov 13 2007
a:=proc(n) local nn: nn:=convert(n,base,10): if 0 < nn[1] and `mod`(n,nn[1]^2) =0 then n else end if end proc: seq(a(n),n=1..250); # Emeric Deutsch, Nov 15 2007

Mathematica

Select[Range[250], IntegerDigits[ # ][[ -1]] > 0 && Mod[ #, IntegerDigits[ # ][[ -1]]^2] == 0 &] (* Stefan Steinerberger, Nov 12 2007 *)
dsldQ[n_]:=Module[{lidnsq=Last[IntegerDigits[n]]^2},lidnsq!=0 && Divisible[n,lidnsq]]; Select[Range[300],dsldQ] (* Harvey P. Dale, May 03 2011 *)

PARI

is(n)=n%(n%10)^2==0 \\ Charles R Greathouse IV, Dec 28 2011

Python

def ok(n): return n%10 > 0 and n%(n%10)**2 == 0
print([k for k in range(273) if ok(k)]) # Michael S. Branicky, Jul 03 2022

R

which(sapply(1:500,function(x) isint(x/(x%%10)^2))) # Christian N. K. Anderson, May 04 2013

Formula

Numbers k such that fp[k / (k mod 10)] = 0.

a(n) ~ 6350400*n/1241929 = 5.113...*n. - Charles R Greathouse IV, Dec 28 2011

Extensions

Corrected and extended by Stefan Steinerberger, Emeric Deutsch and R. J. Mathar, Nov 12 2007