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Number of ways writing n^n as a product of decimal digits of some other number which has no digits equal to 1.
3

%I #9 Feb 01 2024 20:03:14

%S 0,2,3,81,1,102136,1,1389537,4181,4972825,0,12718670252691776,0,

%T 4506838380,11472991008,53560898629395777,0,514875062240230100091396,

%U 0,164997736300578242823300,241098942106440,0,0,3203410440031870942324022423896806853153460,1,0,61305790721611591

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

%C 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.

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

%e 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.

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

%K base,nonn

%O 1,2

%A _Labos Elemer_, Feb 19 2002

%E Edited By _Henry Bottomley_, Feb 26 2002.

%E Edited and extended by _Max Alekseyev_, Sep 19 2009

%E a(9) corrected by _Sean A. Irvine_, Feb 01 2024