A199745 Numbers such that the sum of the largest and the smallest prime divisor equals the sum of the other distinct prime divisors.

2145, 2730, 4641, 4845, 5005, 5460, 5610, 6435, 7410, 8190, 8778, 9177, 10725, 10920, 11220, 11305, 11730, 13485, 13585, 13650, 13923, 14535, 14820, 16380, 16830, 17017, 17556, 19110, 19305, 20010, 20930, 21489, 21505, 21840, 22230, 22440, 23460, 23529, 23595

Offset: 1

Author

Michel Lagneau, Nov 09 2011

Keywords

• nonn

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.

Examples

			22440 is in the sequence because the distinct prime divisors are  {2, 3, 5, 11, 17} and 17+2 = 3+5+11.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020639, A006530, A074320, A008472, A109353.

Programs

Haskell

a199745 n = a199745_list !! (n-1)
a199745_list = filter (\x -> 2 * (a074320 x) == a008472 x) [1..]
-- Reinhard Zumkeller, Nov 10 2011

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 *)

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

Formula

n such that A008472(n)/2 = A074320(n) = A020639(n) + A006530 (n). - Ray Chandler, Nov 10 2011

Sum_{k=2..A001221(a(n))} A027748(a(n),k) = A027748(a(n),1) + A027748(a(n), A001221(a(n))). - Reinhard Zumkeller, Nov 10 2011