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A068186
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a(n) is the largest number whose product of decimal digits equals n^n.
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3
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22, 333, 22222222, 55555, 333333222222, 7777777, 222222222222222222222222, 333333333333333333, 55555555552222222222, 0, 333333333333222222222222222222222222, 0, 7777777777777722222222222222
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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2,1
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COMMENTS
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No digit=1 is permitted to avoid infinite number of solutions; a(n)=0 if A067734(n^n)=0.
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LINKS
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Chai Wah Wu, Table of n, a(n) for n = 2..100
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FORMULA
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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.
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EXAMPLE
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n=10, 10^10=10000000000, a(5)=55555555552222222222.
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PROG
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(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
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CROSSREFS
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Cf. A000312, A001222, A002473, A067734, A068183-A068187, A068189-A068191.
Sequence in context: A000461 A216730 A048795 * A021284 A019623 A021794
Adjacent sequences: A068183 A068184 A068185 * A068187 A068188 A068189
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KEYWORD
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base,nonn
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AUTHOR
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Labos Elemer, Feb 19 2002
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EXTENSIONS
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a(12) corrected by Chai Wah Wu, Aug 12 2017
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STATUS
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approved
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