A328287 Number of multiples of n which have only distinct and nonzero digits in base 10.

0, 986409, 438404, 572175, 219202, 109601, 255752, 140515, 109601, 432645, 0, 90212, 127163, 75768, 62436, 65027, 56104, 57930, 194244, 51869, 0, 81493, 40572, 42969, 63654, 27400, 33587, 145926, 31217, 34146, 0, 31827, 27926, 51090, 25772, 15702, 97114, 26330, 23106, 43929, 0, 23983, 36409

Offset: 0

Author

M. F. Hasler, Oct 10 2019

Keywords

• nonn
• base

Comments

This is column 0 of A328288, extension of A328277.

No term can exceed a(1), cf. example. The sequence is finite in the sense that a(n) = 0 for n > 987654321, since one cannot have more than 9 distinct nonzero digits.

See A328290 for generalization to other bases.

Examples

			For n = 1, this is simply the number of numbers with only distinct and nonzero digits. All other terms are less than a(1), namely, the size of the subset of these numbers which are multiples of n.
		

Links

• Rémy Sigrist, PARI program for A328287

Crossrefs

Cf. A328288, A328277.

This is row 10 of A328290.

Programs

PARI

A328287(n,B=10,S)={for(L=1,B-1,my(T=vectorv(L,k,B^(k-1))); forperm(L,p,u=vecextract(T,p);forvec(d=vector(L,i,[1,B-1]),d*u%n||S++,2)));S} \\ 2nd optional argument allows to specify a base different from 10

PARI

See Links section

Formula

a(n) = 0 whenever n == 0 (mod 10) or n > 987654321.