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