A180484 Numbers n such that r*(n/k)^2 is an integer, where n=(x_1 x_2 ... x_r) with x_i the decimal digits of n and k = x_1 * x_2 * ... * x_r.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 15, 24, 36, 111, 112, 115, 128, 132, 135, 144, 175, 212, 216, 224, 312, 315, 384, 432, 612, 624, 672, 735, 816, 1111, 1112, 1113, 1114, 1115, 1116, 1121, 1122, 1124, 1125, 1127, 1128, 1131, 1134, 1144, 1161, 1164, 1176, 1184

Offset: 1

Author

Ctibor O. Zizka, Sep 07 2010

Keywords

• base
• easy
• nonn

Comments

A007602 is a subsequence, with 1114 the first nonmember of A007602. - D. S. McNeil, Sep 09 2010

Examples

			n=36, r=2, 2*(36/3*6)^2=8, n=36 belongs to the sequence.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..19985

Crossrefs

Subsequence of A052382. A007602 is a subsequence.

Programs

Maple

A055642 := proc(n) max(1, ilog10(n)+1) ; end proc:
A007954 := proc(n) mul(d, d= convert(n,base,10)) : end proc:
isA180484 := proc(n) r := A055642(n) ; k := A007954(n) ; if k <> 0 then type(r*n^2/k^2,'integer') ; else false; end if; end proc:
for n from 1 to 2200 do if isA180484(n) then printf("%d,",n) ; end if; end do:
# R. J. Mathar, Sep 08 2010

PARI

is(n)=my(d=digits(n), r=#d, k=vecprod(d)); k && denominator((n/k)^2*r)==1 \\ Charles R Greathouse IV, Jun 03 2020

Python

from gmpy2 import t_mod, mpz
from operator import mul
from functools import reduce
A180484 = [int(mpz(n)) for n in (str(x) for x in range(1, 10**9)) if not
          (n.count('0') or t_mod(mpz(n)**2*len(n),
          reduce(mul, (mpz(d) for d in n))**2))]
# Chai Wah Wu, Aug 26 2014

Extensions

More terms from R. J. Mathar and D. S. McNeil, Sep 08 2010

Updated an A-number in a comment R. J. Mathar, Oct 18 2010