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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A095611 A307534 A200070 * A146081 A249838 A103652

Adjacent sequences:  A324207 A324208 A324209 * A324211 A324212 A324213

KEYWORD

nonn

AUTHOR

David A. Corneth, Apr 09 2019

STATUS

approved

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)