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

1,1

Links

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

Example

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).

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]]&]

Prog

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

Crossrefs

Cf. A071140.

Sequence in context: A335272 A358255 A307534 * A324210 A146081 A249838

Adjacent sequences: A200067 A200068 A200069 * A200071 A200072 A200073

Keyword

nonn

Author

Michel Lagneau, Nov 13 2011

Status

approved