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A118548
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Squares which are divisible by the product of their digits.
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1
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1, 4, 9, 36, 144, 1296, 2916, 11664, 41616, 82944, 186624, 1218816, 2214144, 11614464, 21123216, 21233664, 22127616, 27123264, 49787136, 122943744, 146313216, 171714816, 222129216, 429981696, 812934144, 1316818944
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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2916 is in the sequence because (1) it is a square, (2) the product of its digits is 2*9*1*6=108 and (3) 2916 is divisible by 108.
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MATHEMATICA
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sdpdQ[n_]:=Module[{idn=IntegerDigits[n]}, !MemberQ[idn, 0]&&Divisible[ n, Times@@idn]]; Select[Range[40000]^2, sdpdQ] (* Harvey P. Dale, Jul 04 2013 *)
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PROG
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(Python)
from operator import mul
from functools import reduce
from gmpy2 import t_mod, mpz
A118548 = [n for n in (x**2 for x in range(1, 10**6)) if not (str(n).count('0') or t_mod(n, reduce(mul, (mpz(d) for d in str(n)))))]
(PARI) lista(nn) = {for (n=1, nn, sq = n^2; d = digits(sq); p = prod(k=1, #d, d[k]); if (p && !(sq % p), print1(sq, ", ")); ); } \\ Michel Marcus, Aug 24 2014
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), May 03 2006
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STATUS
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approved
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