A373641 - OEIS

%I #27 Jul 05 2024 11:10:27

%S 1,2,3,10,5,36,7,120,45,90,0,924,0,182,210,3860,0,3060,0,3800,420,0,0,

%T 61824,300,0,3627,10584,0,25230,0,375968,0,0,1190,441000,0,0,0,426400,

%U 0,70602,0,0,44550,0,0,11936496,1176,58800,0,0,0,1491102,0,1638560

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

%C Trivially, for the four single-digit primes p, a(p)=p.

%C 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.

%H Graham Holmes, <a href="/A373641/b373641.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 0 <=> n in { A068191 }.

%F a(n) > 0 <=> n in { A002473 }.

%F a(n) = A163767(n) for n <= 9.

%e a(4) = 10: 1114, 1122, 1141, 1212, 1221, 1411, 2112, 2121, 2211, 4111.

%p b:= proc(n, t, i) option remember; `if`(n=1, 1/t!, `if`(i<2, 0,

%p       add(b(n/i^j, t-j, i-1)/j!, j=0..padic[ordp](n, i))))

%p     end:

%p a:= n-> n!*b(n$2, 9):

%p seq(a(n), n=1..56);  # _Alois P. Heinz_, Jun 12 2024

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

%K nonn,base

%O 1,2

%A _Graham Holmes_, Jun 12 2024