cp's OEIS Frontend

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

%I A199745 #39 Jul 27 2021 04:06:54
%S A199745 2145,2730,4641,4845,5005,5460,5610,6435,7410,8190,8778,9177,10725,
%T A199745 10920,11220,11305,11730,13485,13585,13650,13923,14535,14820,16380,
%U A199745 16830,17017,17556,19110,19305,20010,20930,21489,21505,21840,22230,22440,23460,23529,23595
%N A199745 Numbers such that the sum of the largest and the smallest prime divisor equals the sum of the other distinct prime divisors.
%C A199745 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.
%H A199745 Reinhard Zumkeller, <a href="/A199745/b199745.txt">Table of n, a(n) for n = 1..1000</a>
%F A199745 n such that A008472(n)/2 = A074320(n) = A020639(n) + A006530 (n). - _Ray Chandler_, Nov 10 2011
%F A199745 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
%e A199745 22440 is in the sequence because the distinct prime divisors are  {2, 3, 5, 11, 17} and 17+2 = 3+5+11.
%p A199745 isA199745 := proc(n)
%p A199745   local p;
%p A199745   p := sort(convert(numtheory[factorset](n),list)) ;
%p A199745   if nops(p) >= 3 then
%p A199745     return ( op(1,p) + op(-1,p) = add(op(i,p),i=2..nops(p)-1) ) ;
%p A199745   else
%p A199745     false;
%p A199745   end if;
%p A199745 end proc:
%p A199745 for n from 2 to 20000 do
%p A199745   if isA199745(n) then
%p A199745     printf("%d,",n) ;
%p A199745   end if ;
%p A199745 end do: # _R. J. Mathar_, Nov 10 2011
%t A199745 Select[Range[25000],Plus@@(pl=First/@FactorInteger[#])/2==pl[[1]]+pl[[-1]]&] (* _Ray Chandler_, Nov 10 2011 *)
%o A199745 (Sage)
%o A199745 def isA199745(n) :
%o A199745     p = factor(n)
%o A199745     return len(p) > 2 and p[0][0] + p[-1][0] == add(p[i][0] for i in (1..len(p)-2))
%o A199745 [n for n in (2..20000) if isA199745(n)]  # _Peter Luschny_, Nov 10 2011
%o A199745 (Haskell)
%o A199745 a199745 n = a199745_list !! (n-1)
%o A199745 a199745_list = filter (\x -> 2 * (a074320 x) == a008472 x) [1..]
%o A199745 -- _Reinhard Zumkeller_, Nov 10 2011
%Y A199745 Cf. A020639, A006530, A074320, A008472, A109353.
%K A199745 nonn
%O A199745 1,1
%A A199745 _Michel Lagneau_, Nov 09 2011