A339439 Number of n-digit numbers (in base 10) that are divisible by each of their nonzero digits.

1, 9, 23, 105, 614, 3826, 25373, 177247, 1288440, 9679469, 74720569, 590162149, 4753928352, 38956270302, 324107031605, 2733414294539, 23338817531394, 201537057920381, 1758534957457627, 15493080163102862, 137729286979112861, 1234692470638216407, 11155826203456047704

Offset: 0

Author

Phuc H. G. Trinh, Dec 04 2020

Keywords

• nonn
• base

Examples

			a(2) = 23: 10, 11, 12, 15, 20, 22, 24, 30, 33, 36, 40, 44, 48, 50, 55, 60, 66, 70, 77, 80, 88, 90, 99.
		

Crossrefs

Cf. A002796.

Programs

PARI

C(digs,n,m)={my(v=vector(m)); v[1]=1; for(i=1, n, v=vector(m, j, sum(k=1, #digs, my(r=10^(i-1)*digs[k]%m); v[1+(j-1-r)%m]))); v}
a(n)={if(n==1, 10, my(m=lcm([2..9])); sumdiv(m, d, my(digs=select(t->t<=1||d%t==0, [0..9])); my(v=C(digs,n,m)-C(digs,n-1,m)); sum(i=1, m/d, if(gcd(m/d,i)==1, v[1+i*d%m]))))} \\ Andrew Howroyd, Dec 04 2020

Extensions

Terms a(18) and beyond from Andrew Howroyd, Dec 04 2020