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A256115 Zeroless numbers n whose digit product squared is equal to the digit product of n^2.

%I A256115 #34 Apr 12 2020 06:14:57
%S A256115 1,2,3,661,983,2631,2893,9254,9628,9642,11892,12385,12893,13836,14642,
%T A256115 14661,16472,18615,27519,29474,35383,36213,36914,38691,43386,46215,
%U A256115 49231,49342,56176,72576,75384,76256,83631,87291,92843,94482,99146,99482,99842,113865
%N A256115 Zeroless numbers n whose digit product squared is equal to the digit product of n^2.
%H A256115 David A. Corneth, <a href="/A256115/b256115.txt">Table of n, a(n) for n = 1..10000</a>
%t A256115 fQ[n_] := Block[{d = Times @@ IntegerDigits@ n}, And[d != 0, d^2 == Times @@ IntegerDigits[n^2]]]; Select[Range@ 120000, fQ] (* _Michael De Vlieger_, Apr 22 2015 *)
%o A256115 (Python)
%o A256115 def product_digits(n):
%o A256115     results = 1
%o A256115     while n > 0:
%o A256115         remainder = n % 10
%o A256115         results *= remainder
%o A256115         n = (n-remainder)/10
%o A256115     return results
%o A256115 L = []
%o A256115 for a in range(1, 100000):
%o A256115     if product_digits(a*a) == (product_digits(a))*(product_digits(a)) and (product_digits(a) > 0):
%o A256115         L.append(a)
%o A256115 print(L)
%o A256115 (Sage)
%o A256115 [x for x in [1..50000] if (0 not in x.digits()) and prod(x.digits())^2==prod((x^2).digits())] # _Tom Edgar_, Apr 03 2015
%o A256115 (PARI) is(n)=vecmin(digits(n))&&A007954(n)^2==A007954(n^2) \\ _M. F. Hasler_, Apr 22 2015
%Y A256115 Cf. A007954, A052382, A256114.
%K A256115 nonn,easy,base
%O A256115 1,2
%A A256115 _Reiner Moewald_, Mar 15 2015