A167620 Numbers that are multiples of their digital product, where this digital product also appears as their least significant digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 111, 112, 115, 315, 612, 1111, 1112, 1113, 1115, 1116, 11111, 11112, 11115, 12312, 13212, 21312, 23112, 31212, 32112, 111111, 111112, 111115, 111315, 111612, 113115, 116112, 131115, 161112, 311115, 511175

Offset: 1

Author

Claudio Meller, Nov 07 2009

Keywords

• nonn
• base

Comments

Subsequence of A007602. - R. J. Mathar, Nov 12 2009

The digital products of the terms are a subsequence of A238985. - Karl-Heinz Hofmann, Feb 16 2024

Examples

			612 is in the list because 6*1*2=12, 612 is a multiple of 12, and 12 is the final two digits of 612.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..8042 (Terms < 10^18, first 690 terms from David A. Corneth)

Crossrefs

Cf. A007602, A238985, A194356.

Programs

PARI

is(n) = { my(vp = vecprod(digits(n))); vp != 0 && n %vp == 0 && n % 10^(#digits(vp)) == vp } \\ David A. Corneth, Mar 30 2021

Python

A167620 = []
for k in range(1,511176):
    dprod, k_str = 1, str(k)
    for d in range(0,len(k_str)): dprod *= int(k_str[d])
    if dprod != 0 and k % dprod == 0 and str(dprod) == k_str[-(len(str(dprod))):]:
        A167620.append(k)
print(A167620) # Karl-Heinz Hofmann, Jan 26 2024