OFFSET
1,1
COMMENTS
Equal to the indices of the zero terms that correspond to composite numbers in A191906.
LINKS
Robert Israel, Table of n, a(n) for n = 1..1203
EXAMPLE
12 is on the list because the proper divisors of 12 are [1,2,3,4,6]. The product of these numbers is 144. Their sum is 16. 144 is divisible by 16.
MAPLE
filter:= proc(n)
local d, p, s;
if isprime(n) then return false fi;
d:= numtheory:-divisors(n) minus {n};
convert(d, `*`) mod convert(d, `+`) = 0;
end proc:
select(filter, [$2..10000]); # Robert Israel, Dec 16 2014
MATHEMATICA
a247145[n_Integer] :=
Select[Select[Range[n], CompositeQ[#] &],
Divisible[Times @@ Most@Divisors[#], Plus @@ Most@Divisors[#]] &]; a247145[4680] (* Michael De Vlieger, Dec 15 2014 *)
fQ[n_Integer] := Block[{d = Most@Divisors@n}, Mod[Times @@ d, Plus @@ d] == 0]; Select[Range@4680, ! PrimeQ@# && fQ@# &] (* Michael De Vlieger, Dec 19 2014, suggested by Robert G. Wilson v *)
PROG
(Python)
from functools import reduce
from operator import mul
def divs(n):
for i in range(1, int(n / 2 + 1)):
if n % i == 0:
yield i
yield n
g = []
for a in range(2, 100):
q = list(divs(a))[0:-1]
if reduce(mul, q, 1) % sum(q) == 0 and len(q) != 1:
g.append(a)
print(g)
(PARI) forcomposite(n=1, 10^3, d=divisors(n); p=prod(i=1, #d-1, d[i]); if(!(p%(sigma(n)-n)), print1(n, ", "))) \\ Derek Orr, Nov 27 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Consiglio, Jr., Nov 20 2014
EXTENSIONS
More terms from Derek Orr, Dec 03 2014
STATUS
approved