A068186 a(n) is the largest number whose product of decimal digits equals n^n.

22, 333, 22222222, 55555, 333333222222, 7777777, 222222222222222222222222, 333333333333333333, 55555555552222222222, 0, 333333333333222222222222222222222222, 0, 7777777777777722222222222222

Offset: 2

Author

Labos Elemer, Feb 19 2002

Keywords

• base
• nonn

Comments

No digit=1 is permitted to avoid infinite number of solutions; a(n)=0 if A067734(n^n)=0.

Examples

			n=10, 10^10=10000000000, a(5)=55555555552222222222.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..100

Crossrefs

Cf. A000312, A001222, A002473, A067734, A068183-A068187, A068189-A068191.

Programs

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

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.

Extensions

a(12) corrected by Chai Wah Wu, Aug 12 2017