

A281995


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


1



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
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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: A295307 A073803 A182851 * A304452 A292763 A176175
Adjacent sequences: A281992 A281993 A281994 * A281996 A281997 A281998


KEYWORD

nonn


AUTHOR

K. D. Bajpai, Feb 04 2017


STATUS

approved



