A068185 Number of ways writing n^n as a product of decimal digits of some other number which has no digits equal to 1.

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

Author

Labos Elemer, Feb 19 2002

Keywords

• base
• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A000045, A000073, A000312, A001222, A002473, A067734, A068183-A068187, A068189-A068191.

Formula

a(n) = A067734(n^n) = A067734(A000312(n))

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