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

1, 2, 3, 661, 983, 2631, 2893, 9254, 9628, 9642, 11892, 12385, 12893, 13836, 14642, 14661, 16472, 18615, 27519, 29474, 35383, 36213, 36914, 38691, 43386, 46215, 49231, 49342, 56176, 72576, 75384, 76256, 83631, 87291, 92843, 94482, 99146, 99482, 99842, 113865

Offset: 1

Author

Reiner Moewald, Mar 15 2015

Keywords

• nonn
• easy
• base

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007954, A052382, A256114.

Programs

Mathematica

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 *)

PARI

is(n)=vecmin(digits(n))&&A007954(n)^2==A007954(n^2) \\ M. F. Hasler, Apr 22 2015

Python

def product_digits(n):
    results = 1
    while n > 0:
        remainder = n % 10
        results *= remainder
        n = (n-remainder)/10
    return results
L = []
for a in range(1, 100000):
    if product_digits(a*a) == (product_digits(a))*(product_digits(a)) and (product_digits(a) > 0):
        L.append(a)
print(L)

Sage

[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