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A068187 a(n) is the smallest number such that the product of its decimal digits equals n^n, or 0 if no solutions exist. 9
1, 4, 39, 488, 55555, 88999, 7777777, 88888888, 999999999, 25555555555888, 0, 88888888999999, 0, 4777777777777778888, 35555555555555559999999, 2888888888888888888888, 0, 888888999999999999999999, 0, 2555555555555555555558888888888888, 37777777777777777777779999999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = 0 if and only if n has a prime factor > 7. If n > 1 has no prime factor > 7, let n^n = 2^a*3^b*5^c*7^d. Let m(x) denote the number of digit x in a(n). Then a(n) is a number whose digits are nondecreasing and defined as follows. m(2) = 1 if a mod 3 == 1 and 0 otherwise, m(3) = 1 if b mod 2 == 1 and 0 otherwise, m(4) = 1 if a mod 3 == 2 and 0 otherwise, m(5) = c, m(6) = 0, m(7) = d, m(8) = floor(a/3), m(9) = floor(b/2). - Chai Wah Wu, Aug 12 2017

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..200

PROG

(Python)

from sympy import factorint

def A068187(n):

    if n == 1:

        return 1

    pf = factorint(n)

    return 0 if max(pf) > 7 else int(''.join(sorted(''.join(str(a)*(n*b) for a, b in pf.items()).replace('222', '8').replace('22', '4').replace('33', '9')))) # Chai Wah Wu, Aug 13 2017

CROSSREFS

Cf. A000312, A067734, A068183, A068184, A068185, A068186, A068188, A068190.

Sequence in context: A203211 A214823 A275517 * A177775 A192935 A024055

Adjacent sequences:  A068184 A068185 A068186 * A068188 A068189 A068190

KEYWORD

base,nonn,changed

AUTHOR

Labos Elemer, Feb 18 2002

EXTENSIONS

Edited by Dean Hickerson and Henry Bottomley, Mar 07 2002

STATUS

approved

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Last modified August 22 20:51 EDT 2017. Contains 290951 sequences.