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

1,2

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.

Links

Table of n, a(n) for n=1..27.

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.

Crossrefs

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

Sequence in context: A370993 A371228 A377687 * A037391 A037427 A042549

Adjacent sequences: A068182 A068183 A068184 * A068186 A068187 A068188

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