OFFSET
1,2
COMMENTS
Dividuus : Latin for "divisible" Most of these numbers are even, but there are some odd numbers too. However, none of them seem to end on 7 (except for the obvious number 7 itself). Are there numbers in the sequence ending in 7?
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..2639
EXAMPLE
624 is in the sequence because (1) the sum of its digits is 6+4+2=12, (2) the product of its digits is 6*4*2=48, (3) the digital root is 3, (4) the multiplicative digital root is 6 and 624 is divisible by 12,48,3 and 6.
MAPLE
filter:= proc(n)
local L, s, p;
L:= convert(n, base, 10);
s:= convert(L, `+`);
if n mod s <> 0 then return false fi;
p:= convert(L, `*`);
if p = 0 or n mod p <> 0 then return false fi;
while s > 10 do
s:= convert(convert(s, base, 10), `+`);
od:
if n mod s <> 0 then return false fi;
while p > 10 do
p:= convert(convert(p, base, 10), `*`);
od:
p > 0 and n mod p = 0;
end proc:
select(filter, [$1..10^4]); # Robert Israel, Aug 24 2014
PROG
(Python)
from operator import mul
from functools import reduce
from gmpy2 import t_mod, mpz
def A031347(n):
while n > 9:
n = reduce(mul, (int(d) for d in str(n)))
return n
(str(n).count('0') or t_mod(n, (1+t_mod((n-1), 9))) or
t_mod(n, A031347(n)) or t_mod(n, sum((mpz(d) for d in str(n))))
or t_mod(n, reduce(mul, (mpz(d) for d in str(n)))))]
# Chai Wah Wu, Aug 26 2014
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), May 07 2006
EXTENSIONS
Inserted a(17)=216 by Chai Wah Wu, Aug 24 2014
STATUS
approved