|
|
A048055
|
|
Numbers k such that (sum of the nonprime proper divisors of k) - (sum of prime divisors of k) = k.
|
|
2
|
|
|
532, 945, 2624, 5704, 6536, 229648, 497696, 652970, 685088, 997408, 1481504, 11177984, 32869504, 52813084, 132612224, 224841856, 2140668416, 2404135424, 2550700288, 6469054976, 9367192064, 19266023936, 23414463358, 31381324288, 45812547584, 55620289024
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
A term of this sequence is a Zumkeller number (A083207) since the set of its divisors can be partitioned into two disjoint parts so that the sums of the two parts are equal.
1 + sigma*(k) = sigma'(k) + k
sigma*(k) := Sum_{1 < d < k, d|k, d not prime}, (A060278),
sigma'(k) := Sum_{1 < d < k, d|k, d prime}, (A105221). (End)
|
|
LINKS
|
|
|
EXAMPLE
|
532 = 1 - 2 + 4 - 7 + 14 - 19 + 28 + 38 + 76 + 133 + 266.
|
|
MAPLE
|
with(numtheory): A048055 := proc(n) local k;
if sigma(n)=2*(n+add(k, k=select(isprime, divisors(n))))
then n else NULL fi end: seq(A048055(i), i=1..7000);
|
|
MATHEMATICA
|
|
|
PROG
|
(Haskell)
import Data.List (partition)
a048055 n = a048055_list !! (n-1)
a048055_list = [x | x <- a002808_list,
let (us, vs) = partition ((== 1) . a010051) $ a027751_row x,
sum us + x == sum vs]
(Python)
from sympy import divisors, primefactors
for n in range(1, 10**4):
....s = sum(divisors(n))
....if not s % 2 and 2*n <= s and (s-2*n)/2 == sum(primefactors(n)):
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|