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
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
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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