A354081 Positive integers k such that the first digit of k is divisible by the product of all the remaining digits of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 21, 22, 31, 33, 41, 42, 44, 51, 55, 61, 62, 63, 66, 71, 77, 81, 82, 84, 88, 91, 93, 99, 111, 211, 212, 221, 311, 313, 331, 411, 412, 414, 421, 422, 441, 511, 515, 551, 611, 612, 613, 616, 621, 623, 631, 632, 661, 711, 717, 771

Offset: 1

Author

Moosa Nasir, Jun 05 2022

Keywords

• nonn
• base

Examples

			9331 is a term: the first digit is 9, which is divisible by the product of the remaining digits, i.e., 3*3*1 = 9.
8448 is not a term: the first digit is 8, which is not divisible by the product of the remaining digits, i.e., 4*4*8 = 128.
		

Crossrefs

Subsequence of A052382.

Programs

Mathematica

Select[Range[1000], !MemberQ[d = IntegerDigits[#], 0] && Divisible[First[d], Times @@ Rest[d]] &] (* Amiram Eldar, Jun 09 2022 *)

PARI

isok(k) = my(d=digits(k), p=vecprod(d)); p && ((d[1] % (p/d[1])) == 0); \\ Michel Marcus, Jun 06 2022

Python

from math import prod
def ok(n):
    d = list(map(int, str(n)))
    return 0 not in d and int(d[0])%prod(d[1:]) == 0
print([k for k in range(800) if ok(k)]) # Michael S. Branicky, Jun 09 2022