A200070 - OEIS

A200070

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

%I #19 Apr 10 2019 04:42:59

%S 110,182,220,364,374,440,494,550,728,748,782,880,988,1100,1210,1274,

%T 1334,1456,1496,1564,1760,1976,2200,2294,2366,2420,2548,2668,2750,

%U 2912,2992,3128,3182,3520,3854,3952,4114,4400,4588,4732,4840,4982,5096,5336,5500

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

%H Robert Israel, <a href="/A200070/b200070.txt">Table of n, a(n) for n = 1..10000</a>

%e 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).

%p filter:= proc(n) local P; P:= numtheory:-factorset(n);

%p convert(P,`+`) = 2*(max(P)-min(P))

%p end proc:

%p select(filter, [$1..10000]); # _Robert Israel_, Apr 09 2019

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

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

%Y Cf. A071140.

%K nonn

%O 1,1

%A _Michel Lagneau_, Nov 13 2011