A200070 Numbers n such that the sum of the prime divisors equals 2 times the difference between the largest and the smallest prime divisor.

110, 182, 220, 364, 374, 440, 494, 550, 728, 748, 782, 880, 988, 1100, 1210, 1274, 1334, 1456, 1496, 1564, 1760, 1976, 2200, 2294, 2366, 2420, 2548, 2668, 2750, 2912, 2992, 3128, 3182, 3520, 3854, 3952, 4114, 4400, 4588, 4732, 4840, 4982, 5096, 5336, 5500

Offset: 1

Author

Michel Lagneau, Nov 13 2011

Keywords

• nonn

Examples

			98420 is in the sequence because the prime divisors are 2, 5, 7, 19, 37 and the sum 2 + 5 + 7 + 19 + 37 = 70 = 2*(37 - 2).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071140.

Programs

Maple

filter:= proc(n) local P; P:= numtheory:-factorset(n);
  convert(P,`+`) = 2*(max(P)-min(P))
end proc:
select(filter, [$1..10000]); # Robert Israel, Apr 09 2019

Mathematica

Select[Range[5500],Plus@@((pl=First/@FactorInteger[#])/2)==pl[[-1]]-pl[[1]]&]

PARI

isok(n) = if (n>1, my(f=factor(n)[,1]); 2*(vecmax(f) - vecmin(f)) == vecsum(f)); \\ Michel Marcus, Apr 10 2019