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

1,2

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

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A007602, A238985, A194356.

Sequence in context: A007602 A343681 A337941 * A169935 A193498 A361181

Adjacent sequences: A167617 A167618 A167619 * A167621 A167622 A167623

Keyword

nonn,base

Author

Claudio Meller, Nov 07 2009

Status

approved