A281995 - OEIS

%I #18 Feb 16 2017 03:18:40

%S 1,3,5,6,7,10,11,13,14,15,17,19,21,22,23,26,29,31,33,34,35,37,38,39,

%T 41,43,46,47,51,53,55,57,58,59,61,62,65,66,67,69,71,73,74,77,79,83,85,

%U 86,87,89,91,93,94,95,97,101,103,106,107,109,111,113,114,115,118

%N Squarefree numbers that, when added to the sum of their prime factors, remain squarefree.

%H Robert Israel, <a href="/A281995/b281995.txt">Table of n, a(n) for n = 1..10000</a>

%e a(6) = 10 = 2*5 that is squarefree. 10 + 2 + 5 = 17 = 1*17, which is also squarefree.

%e a(14) = 22 = 2*11 that is squarefree. 22 + 2 + 11 = 35 = 5*7, which is also squarefree.

%e a(219) = 434 = 2*7*31 that is squarefree. 434 + 2 + 7 + 31 = 474 = 2*3*79, which is also squarefree.

%p filter:= n -> numtheory:-issqrfree(n) and numtheory:-issqrfree(n+convert(numtheory:-factorset(n),`+`)):

%p select(filter, [$1..1000]); # _Robert Israel_, Feb 15 2017

%t Select[Range[500], SquareFreeQ[#] && SquareFreeQ[# + Total[Times @@@ FactorInteger[#]]] &]

%o (PARI) isok(n) = issquarefree(n) && issquarefree(n + vecsum(factor(n)[, 1])); \\ _Michel Marcus_, Feb 05 2017

%Y Cf. A001414, A005117, A050703.

%K nonn

%O 1,2

%A _K. D. Bajpai_, Feb 04 2017