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

1,2

Links

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

Example

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.

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[#]]] &]

Prog

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

Crossrefs

Cf. A001414, A005117, A050703.

Sequence in context: A073803 A336353 A182851 * A304452 A292763 A176175

Adjacent sequences: A281992 A281993 A281994 * A281996 A281997 A281998

Keyword

nonn

Author

K. D. Bajpai, Feb 04 2017

Status

approved