A199857 Numbers such that the sum of the squares of the largest and the smallest prime divisor equals the sum of the squares of the other distinct prime divisors.

24871, 81719, 81809, 88711, 174097, 198679, 201761, 256151, 273581, 290191, 329681, 405449, 422807, 428281, 472549, 572663, 592999, 604279, 620977, 701561, 728119, 752191, 770431, 876641, 898909, 1011839, 1063517, 1121729, 1178879, 1218679, 1251439, 1389223

Offset: 1

Author

Michel Lagneau, Nov 11 2011

Keywords

• nonn

Examples

			24871 is in the sequence because the prime distinct divisors are {7, 11, 17, 19} and 19^2 + 7^2 = 11^2 + 17^2 = 410.
Although the early terms are all odd with four distinct prime factors, 7212590 = 2 * 5 * 7 * 11 * 17 * 19 * 29 has seven distinct prime factors, and 2^2 + 29^2 = 5^2 + 7^2 + 11^2 + 17^2 + 19^2 = 845. - _D. S. McNeil_, Nov 12 2011
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A199745.

Programs

Maple

isA199857 := proc(n)
local p;
p := sort(convert((numtheory[factorset](n)), list)) ;
if nops(p) >= 3 then
return ( op(1, p)^2 + op(-1, p)^2 = add(op(i, p)^2, i=2..nops(p)-1) ) ;
else
false;
end if;
end proc:
for n from 2 to 1500000 do
if isA199857(n) then
printf("%d, ", n) ;
end if ;
end do: # program from R. J. Mathar adapted for this sequence - see A199745

Mathematica

Select[Range[1400000], Plus@@((pl=First/@FactorInteger[#])^2/2) == pl[[1]]^2+pl[[-1]]^2&] (* program from Ray Chandler adapted for this sequence - see A199745 *)