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%I #42 Jul 04 2022 01:36:27
%S 1,11,12,21,25,31,32,36,41,51,52,61,63,64,71,72,75,81,91,92,101,111,
%T 112,121,125,128,131,132,141,144,147,151,152,153,161,171,172,175,181,
%U 191,192,201,211,212,216,221,224,225,231,232,241,243,251,252,261,271,272
%N Numbers divisible by the square of their last decimal digit.
%C 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
%C This is a 10-automatic sequence. - _Charles R Greathouse IV_, Dec 28 2011
%H T. D. Noe and Christian N. K. Anderson, <a href="/A132359/b132359.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 values from T. D. Noe)
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F Numbers k such that fp[k / (k mod 10)] = 0.
%F a(n) ~ 6350400*n/1241929 = 5.113...*n. - _Charles R Greathouse IV_, Dec 28 2011
%e 147 belongs to the sequence because 147/7^2 = 3.
%p 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
%p 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
%t Select[Range[250], IntegerDigits[ # ][[ -1]] > 0 && Mod[ #, IntegerDigits[ # ][[ -1]]^2] == 0 &] (* _Stefan Steinerberger_, Nov 12 2007 *)
%t dsldQ[n_]:=Module[{lidnsq=Last[IntegerDigits[n]]^2},lidnsq!=0 && Divisible[n,lidnsq]]; Select[Range[300],dsldQ] (* _Harvey P. Dale_, May 03 2011 *)
%o (PARI) is(n)=n%(n%10)^2==0 \\ _Charles R Greathouse IV_, Dec 28 2011
%o (R) which(sapply(1:500,function(x) isint(x/(x%%10)^2))) # _Christian N. K. Anderson_, May 04 2013
%o (Python)
%o def ok(n): return n%10 > 0 and n%(n%10)**2 == 0
%o print([k for k in range(273) if ok(k)]) # _Michael S. Branicky_, Jul 03 2022
%Y Cf. A034709, A225722, A221651, A225296, A225297, A034709, A034837, A005349, A007602, A034838, A225297.
%K base,easy,nonn,nice
%O 1,2
%A _Jonathan Vos Post_, Nov 08 2007
%E Corrected and extended by _Stefan Steinerberger_, _Emeric Deutsch_ and _R. J. Mathar_, Nov 12 2007
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