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A373641
The number of positive n-digit integers whose digit product is n.
1
1, 2, 3, 10, 5, 36, 7, 120, 45, 90, 0, 924, 0, 182, 210, 3860, 0, 3060, 0, 3800, 420, 0, 0, 61824, 300, 0, 3627, 10584, 0, 25230, 0, 375968, 0, 0, 1190, 441000, 0, 0, 0, 426400, 0, 70602, 0, 0, 44550, 0, 0, 11936496, 1176, 58800, 0, 0, 0, 1491102, 0, 1638560
OFFSET
1,2
COMMENTS
Trivially, for the four single-digit primes p, a(p)=p.
It's not possible by definition to have a digit product equal to a prime number greater than 10, so a(p)=0 for prime p > 10.
LINKS
FORMULA
a(n) = 0 <=> n in { A068191 }.
a(n) > 0 <=> n in { A002473 }.
a(n) = A163767(n) for n <= 9.
EXAMPLE
a(4) = 10: 1114, 1122, 1141, 1212, 1221, 1411, 2112, 2121, 2211, 4111.
MAPLE
b:= proc(n, t, i) option remember; `if`(n=1, 1/t!, `if`(i<2, 0,
add(b(n/i^j, t-j, i-1)/j!, j=0..padic[ordp](n, i))))
end:
a:= n-> n!*b(n$2, 9):
seq(a(n), n=1..56); # Alois P. Heinz, Jun 12 2024
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Graham Holmes, Jun 12 2024
STATUS
approved