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

0,2

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.

Links

Table of n, a(n) for n=0..42.

Rémy Sigrist, PARI program for A328287

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A328288, A328277.

This is row 10 of A328290.

Sequence in context: A206185 A205367 A328288 * A083395 A106782 A154674

Adjacent sequences: A328284 A328285 A328286 * A328288 A328289 A328290

Keyword

nonn,base

Author

M. F. Hasler, Oct 10 2019

Status

approved