OFFSET
1,2
LINKS
Jean-Marie De Koninck and Florian Luca, Positive integers divisible by the product of their nonzero digits, Port. Math. 64 (2007) 75-85. (This proof for upper bounds contains an error. See the paper below.)
Jean-Marie De Koninck and Florian Luca, Corrigendum to "Positive integers divisible by the product of their nonzero digits", Portugaliae Math. 64 (2007), 1: 75-85, Port. Math. 74 (2017), 169-170.
EXAMPLE
For the perfect square 1024 = 32^2 the product of its nonzero digits is 8 which divides 1024.
MATHEMATICA
Select[Range[500]^2, Divisible[#, Times @@ Select[IntegerDigits[#], #1 > 0 &]] &] (* Amiram Eldar, Jul 23 2021 *)
PROG
(Python)
from math import prod
def nzpd(n): return prod([int(d) for d in str(n) if d != '0'])
def ok(sqr): return sqr > 0 and sqr%nzpd(sqr) == 0
print(list(filter(ok, (i*i for i in range(541))))) # Michael S. Branicky, Jul 23 2021
(PARI) isok(m) = issquare(m) && !(m % vecprod(select(x->(x>0), digits(m))));
lista(nn) = for (m=1, nn, if (isok(m^2), print1(m^2, ", "))); \\ Michel Marcus, Jul 23 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Michael Gohn, Joshua Harrington, Sophia Lebiere, Hani Samamah, Kyla Shappell, Wing Hong Tony Wong, Jul 23 2021
STATUS
approved