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A132359
Numbers divisible by the square of their last decimal digit.
7
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
1,2
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
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)
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
EXAMPLE
147 belongs to the sequence because 147/7^2 = 3.
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 *)
PROG
(PARI) is(n)=n%(n%10)^2==0 \\ Charles R Greathouse IV, Dec 28 2011
(R) which(sapply(1:500, function(x) isint(x/(x%%10)^2))) # Christian N. K. Anderson, May 04 2013
(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
KEYWORD
base,easy,nonn,nice
AUTHOR
Jonathan Vos Post, Nov 08 2007
EXTENSIONS
Corrected and extended by Stefan Steinerberger, Emeric Deutsch and R. J. Mathar, Nov 12 2007
STATUS
approved