login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A247145 Composite numbers such that the product of the number's proper divisors is divisible by the sum of the number's proper divisors. 1
6, 12, 24, 28, 40, 42, 56, 60, 90, 120, 140, 153, 216, 234, 270, 290, 360, 440, 496, 522, 568, 585, 588, 672, 708, 819, 924, 984, 992, 1001, 1170, 1316, 1320, 1365, 1431, 1780, 2016, 2184, 2295, 2296, 2299, 2464, 2466, 2655, 2832, 3100, 3344, 3420, 3627, 3724, 3948, 4320, 4336, 4416, 4680 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Equal to the indices of the zero terms that correspond to composite numbers in A191906.
LINKS
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
Cf. A145551.
Sequence in context: A094185 A074902 A096366 * A188158 A061822 A226453
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Derek Orr, Dec 03 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)