OFFSET
1,1
COMMENTS
The definition implies that members of the sequence have at least four distinct prime factors. An even term must have at least five distinct prime factors.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
22440 is in the sequence because the distinct prime divisors are {2, 3, 5, 11, 17} and 17+2 = 3+5+11.
MAPLE
isA199745 := proc(n)
local p;
p := sort(convert(numtheory[factorset](n), list)) ;
if nops(p) >= 3 then
return ( op(1, p) + op(-1, p) = add(op(i, p), i=2..nops(p)-1) ) ;
else
false;
end if;
end proc:
for n from 2 to 20000 do
if isA199745(n) then
printf("%d, ", n) ;
end if ;
end do: # R. J. Mathar, Nov 10 2011
MATHEMATICA
Select[Range[25000], Plus@@(pl=First/@FactorInteger[#])/2==pl[[1]]+pl[[-1]]&] (* Ray Chandler, Nov 10 2011 *)
PROG
(Sage)
def isA199745(n) :
p = factor(n)
return len(p) > 2 and p[0][0] + p[-1][0] == add(p[i][0] for i in (1..len(p)-2))
[n for n in (2..20000) if isA199745(n)] # Peter Luschny, Nov 10 2011
(Haskell)
a199745 n = a199745_list !! (n-1)
a199745_list = filter (\x -> 2 * (a074320 x) == a008472 x) [1..]
-- Reinhard Zumkeller, Nov 10 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 09 2011
STATUS
approved