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%I #21 Jun 03 2020 16:37:02
%S 1,2,3,4,5,6,7,8,9,11,12,15,24,36,111,112,115,128,132,135,144,175,212,
%T 216,224,312,315,384,432,612,624,672,735,816,1111,1112,1113,1114,1115,
%U 1116,1121,1122,1124,1125,1127,1128,1131,1134,1144,1161,1164,1176,1184
%N Numbers n such that r*(n/k)^2 is an integer, where n=(x_1 x_2 ... x_r) with x_i the decimal digits of n and k = x_1 * x_2 * ... * x_r.
%C A007602 is a subsequence, with 1114 the first nonmember of A007602. - _D. S. McNeil_, Sep 09 2010
%H Chai Wah Wu, <a href="/A180484/b180484.txt">Table of n, a(n) for n = 1..19985</a>
%e n=36, r=2, 2*(36/3*6)^2=8, n=36 belongs to the sequence.
%p A055642 := proc(n) max(1, ilog10(n)+1) ; end proc:
%p A007954 := proc(n) mul(d, d= convert(n,base,10)) : end proc:
%p isA180484 := proc(n) r := A055642(n) ; k := A007954(n) ; if k <> 0 then type(r*n^2/k^2,'integer') ; else false; end if; end proc:
%p for n from 1 to 2200 do if isA180484(n) then printf("%d,",n) ; end if; end do:
%p # _R. J. Mathar_, Sep 08 2010
%o (Python)
%o from gmpy2 import t_mod, mpz
%o from operator import mul
%o from functools import reduce
%o A180484 = [mpz(n) for n in (str(x) for x in range(1,10**9)) if not
%o ..........(n.count('0') or t_mod(mpz(n)**2*len(n),
%o ..........reduce(mul, (mpz(d) for d in n))**2))]
%o # _Chai Wah Wu_, Aug 26 2014
%o (PARI) is(n)=my(d=digits(n), r=#d, k=vecprod(d)); k && denominator((n/k)^2*r)==1 \\ _Charles R Greathouse IV_, Jun 03 2020
%Y Subsequence of A052382. A007602 is a subsequence.
%K base,easy,nonn
%O 1,2
%A _Ctibor O. Zizka_, Sep 07 2010
%E More terms from _R. J. Mathar_ and _D. S. McNeil_, Sep 08 2010
%E Updated an A-number in a comment _R. J. Mathar_, Oct 18 2010
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