A281995 Squarefree numbers that, when added to the sum of their prime factors, remain squarefree.

1, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 31, 33, 34, 35, 37, 38, 39, 41, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65, 66, 67, 69, 71, 73, 74, 77, 79, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 101, 103, 106, 107, 109, 111, 113, 114, 115, 118

Offset: 1

Author

K. D. Bajpai, Feb 04 2017

Keywords

• nonn

Examples

			a(6) = 10 = 2*5 that is squarefree. 10 + 2 + 5 = 17 = 1*17, which is also squarefree.
a(14) = 22 = 2*11 that is squarefree. 22 + 2 + 11 = 35 = 5*7, which is also squarefree.
a(219) = 434 = 2*7*31 that is squarefree. 434 + 2 + 7 + 31 = 474 = 2*3*79, which is also squarefree.
		

Links

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

Crossrefs

Cf. A001414, A005117, A050703.

Programs

Maple

filter:= n -> numtheory:-issqrfree(n) and numtheory:-issqrfree(n+convert(numtheory:-factorset(n),`+`)):
select(filter, [$1..1000]); # Robert Israel, Feb 15 2017

Mathematica

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

PARI

isok(n) = issquarefree(n) && issquarefree(n + vecsum(factor(n)[, 1])); \\ Michel Marcus, Feb 05 2017