A339498 Number of zeroless strictly pandigital numbers divisible by the n-th prime.

161280, 362880, 40320, 51752, 31680, 27776, 21271, 19138, 15788, 12613, 11707, 9072, 8832, 8423, 7725, 6822, 6241, 5937, 5454, 5113, 4796, 4629, 4310, 4122, 3744, 3168, 3528, 3410, 3305, 3160, 2826, 2827, 2778, 2619, 2316, 2297, 2297, 2173, 2163, 2094, 2077, 2027, 1879, 1915, 1836, 1780, 1773

Offset: 1

Author

G. L. Honaker, Jr., Dec 07 2020

Keywords

• nonn
• base

Comments

Calculated by Chuck Gaydos.

a(4620), for prime(4620) = 44449, is the first zero entry. The last nonzero entry is a(6289143) for prime 109739359 = 987654231 / 9. - Michael S. Branicky, Dec 07 2020

Crossrefs

Cf. A000040, A050289.

Programs

Python

from sympy import prime
from itertools import permutations
def zeroless_pans():
    for p in permutations("123456789"):
        yield int("".join(p))
def a(n):
    pn = prime(n)
    return sum(zlp%pn==0 for zlp in zeroless_pans())
print([a(n) for n in range(1, 43)]) # Michael S. Branicky, Dec 07 2020