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A068186
a(n) is the largest number whose product of decimal digits equals n^n.
3
22, 333, 22222222, 55555, 333333222222, 7777777, 222222222222222222222222, 333333333333333333, 55555555552222222222, 0, 333333333333222222222222222222222222, 0, 7777777777777722222222222222
OFFSET
2,1
COMMENTS
No digit=1 is permitted to avoid infinite number of solutions; a(n)=0 if A067734(n^n)=0.
LINKS
FORMULA
a(n) is obtained as prime factors of n^n concatenated in order of magnitude and with repetitions; a(n)=0 if n has p > 7 prime factors.
EXAMPLE
n=10, 10^10=10000000000, a(5)=55555555552222222222.
PROG
(Python)
from sympy import factorint
def A068186(n):
if n == 1:
return 1
pf = factorint(n)
ps = sorted(pf.keys(), reverse=True)
if ps[0] > 7:
return 0
s = ''
for p in ps:
s += str(p)*(n*pf[p])
return int(s) # Chai Wah Wu, Aug 12 2017
KEYWORD
base,nonn
AUTHOR
Labos Elemer, Feb 19 2002
EXTENSIONS
a(12) corrected by Chai Wah Wu, Aug 12 2017
STATUS
approved