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A256115 Zeroless numbers n whose digit product squared is equal to the digit product of n^2. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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 *)

PROG

(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

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

CROSSREFS

Cf. A007954, A052382, A256114.

Sequence in context: A165770 A226148 A108332 * A066685 A076155 A136611

Adjacent sequences:  A256112 A256113 A256114 * A256116 A256117 A256118

KEYWORD

nonn,easy,base

AUTHOR

Reiner Moewald, Mar 15 2015

STATUS

approved

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Last modified July 27 15:29 EDT 2021. Contains 346307 sequences. (Running on oeis4.)