login
A068185
Number of ways writing n^n as a product of decimal digits of some other number which has no digits equal to 1.
3
0, 2, 3, 81, 1, 102136, 1, 1389537, 4181, 4972825, 0, 12718670252691776, 0, 4506838380, 11472991008, 53560898629395777, 0, 514875062240230100091396, 0, 164997736300578242823300, 241098942106440, 0, 0, 3203410440031870942324022423896806853153460, 1, 0, 61305790721611591
OFFSET
1,2
COMMENTS
a(n)= 0 when n has prime-factor larger than 7 [so A067734(n)=0] or when n is in A068191, i.e. not in A002473.
FORMULA
a(n) = A067734(n^n) = A067734(A000312(n))
EXAMPLE
n=1 has no solution; a(2)=A000073(6)=2 with {4,22} solutions; a(3)=A067734(27)=3=Fibonacci[4]; n=5 and n=7, n^n has single prime factor of which any true multiple have 2 digits so 55555 and 7777777 are the only solutions, so a(5)=a(7)=1; a(4)=A067734(256)=81=A000073(10); a(8)=A067734(2^24)=A000073(26)=1389537; n=9 a(9)=A067734(3^27)=4181.
KEYWORD
base,nonn
AUTHOR
Labos Elemer, Feb 19 2002
EXTENSIONS
Edited By Henry Bottomley, Feb 26 2002.
Edited and extended by Max Alekseyev, Sep 19 2009
a(9) corrected by Sean A. Irvine, Feb 01 2024
STATUS
approved