

A328160


Terms k of A112998 such that k+2 is nonsquarefree.


0



61, 73, 277, 421, 2797, 6217, 8521, 9277, 9817, 10357, 11161, 12301, 12841, 13381, 15121, 17377, 17881, 18097, 19861, 25657, 30517, 30661, 33037, 35521, 36241, 36457, 48121, 50821, 51481, 54421, 56437, 58417, 60217, 66601, 66697, 67057, 71341, 74077, 77641, 79801, 88117, 94777, 96181, 98017
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OFFSET

1,1


COMMENTS

Complement of A328137 in A112998.
Each term is either 3*x^22 where x, 3*x^22 and (3*x^21)/2 are prime or it is 9*x2 where x, 9*x2 and (9*x1)/2 are prime.


LINKS

Table of n, a(n) for n=1..44.


EXAMPLE

a(3)=277 is a term because 277 is prime, 277+1=2*139 where 139 is prime, and 279=3^2*31 is a 3almost prime that is nonsquarefree.


MAPLE

N:= 100000:
A1:= map(x > 3*x^22, select(x > isprime(x) and isprime(3*x^22) and isprime((3*x^21)/2), {seq(i, i=3..floor(sqrt((N+2)/3)), 2)})):
A2:= map(x > 9*x2, select(x > isprime(x) and isprime(9*x2) and isprime((9*x1)/2), {seq(i, i=3..(N+2)/9, 2)})):
sort(convert(A1 union A2, list));


MATHEMATICA

Select[Prime@ Range[10^4], And[PrimeOmega /@ {# + 1, # + 2} == {2, 3}, ! SquareFreeQ[# + 2]] &] (* Michael De Vlieger, Oct 06 2019 *)


CROSSREFS

Cf. A112998, A328137.
Sequence in context: A260808 A141457 A112998 * A118162 A217076 A281960
Adjacent sequences: A328157 A328158 A328159 * A328161 A328162 A328163


KEYWORD

nonn


AUTHOR

Robert Israel, Oct 05 2019


STATUS

approved



