A373641 The number of positive n-digit integers whose digit product is n.

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

Graham Holmes, Table of n, a(n) for n = 1..10000

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

Cf. A002033, A002473, A068191, A074206, A163767.

Sequence in context: A078730 A334628 A292239 * A163767 A343936 A336091

Adjacent sequences: A373638 A373639 A373640 * A373642 A373643 A373644

Keyword

nonn,base

Author

Graham Holmes, Jun 12 2024

Status

approved