A324210 Squarefree numbers k such that the sum of the distinct prime factors of k is twice the difference between the largest and the smallest prime factors of k.

110, 182, 374, 494, 782, 1334, 2294, 3182, 3854, 4982, 6254, 7905, 7917, 8174, 9782, 11534, 12765, 14774, 15810, 15834, 18705, 19982, 20757, 21614, 22330, 22454, 24182, 25530, 27265, 28210, 30381, 30597, 32637, 35894, 37410, 40205, 41181, 41514, 43005, 47414, 49210

Offset

1,1

Comments

This sequence is a primitive subsequence of A200070. If p|a(n) for some prime p then p*a(n) is in A200070.

From Robert Israel, Apr 09 2019: (Start)

All terms have at least three prime factors.

The number of prime factors is odd if and only if the term is even.

The terms with three prime factors are 2*A111192. (End)

Links

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

Example

110 = 2 * 5 * 11 is squarefree. The minimal and maximal prime divisors of 110 are 2 and 11 respectively. Twice their difference is 2 * (11-2) = 18 which is also the sum of the distinct prime divisors of 110; 2 + 5 + 11 = 18.

Maple

filter:= proc(n) local P;
if not numtheory:-issqrfree(n) then return false fi;
P:= numtheory:-factorset(n);
  convert(P, `+`) = 2*(max(P)-min(P))
end proc:
select(filter, [$1..50000]); # Robert Israel, Apr 09 2019

Mathematica

Select[Select[Range[2, 5*10^4], SquareFreeQ], Total@ # == 2 (Last@ # - First@ #) &@ FactorInteger[#][[All, 1]] &] (* Michael De Vlieger, Apr 11 2019 *)

Prog

(PARI) is(n) = if(!issquarefree(n), return(0)); my(f=factor(n)[, 1]~); sum(i=1, #f, f[i])==2*(f[#f]-f[1])
forcomposite(c=1, 50000, if(is(c), print1(c, ", "))) \\ Felix Fröhlich, Apr 11 2019

Crossrefs

Cf. A200070, A111192.

Sequence in context: A358255 A307534 A200070 * A146081 A249838 A103652

Adjacent sequences: A324207 A324208 A324209 * A324211 A324212 A324213

Keyword

nonn

Author

David A. Corneth, Apr 09 2019

Status

approved