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A256115 Zeroless numbers n whose digit product squared is equal to the digit product of n^2. 3

%I

%S 1,2,3,661,983,2631,2893,9254,9628,9642,11892,12385,12893,13836,14642,

%T 14661,16472,18615,27519,29474,35383,36213,36914,38691,43386,46215,

%U 49231,49342,56176,72576,75384,76256,83631,87291,92843,94482,99146,99482,99842,113865

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

%H David A. Corneth, <a href="/A256115/b256115.txt">Table of n, a(n) for n = 1..10000</a>

%t 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 (Python)

%o def product_digits(n):

%o results = 1

%o while n > 0:

%o remainder = n % 10

%o results *= remainder

%o n = (n-remainder)/10

%o return results

%o L = []

%o for a in range(1, 100000):

%o if product_digits(a*a) == (product_digits(a))*(product_digits(a)) and (product_digits(a) > 0):

%o L.append(a)

%o print(L)

%o (Sage)

%o [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 (PARI) is(n)=vecmin(digits(n))&&A007954(n)^2==A007954(n^2) \\ _M. F. Hasler_, Apr 22 2015

%Y Cf. A007954, A052382, A256114.

%K nonn,easy,base

%O 1,2

%A _Reiner Moewald_, Mar 15 2015

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Last modified April 13 15:23 EDT 2021. Contains 342936 sequences. (Running on oeis4.)