%I #13 May 17 2024 09:55:53

%S 1,5,6,7,11,13,17,19,23,29,30,31,35,37,41,42,43,47,53,55,59,61,65,66,

%T 67,71,72,73,77,78,79,83,85,89,91,95,97,101,102,103,107,108,109,113,

%U 114,115,119,127,131,133,137,138,139,143,145,149,151,155,157,161

%N Fixed points of A300955.

%C For any n > 0, A279510(A279510(n)) belongs to this sequence (and this sequence is infinite).

%C For any n > 0:

%C - a(n) is a multiple of 2 iff a(n) is a multiple of 3,

%C - if a(n) is a multiple of 2 then A007814(a(n)) = A300955(A007949(a(n))) and A300955(A007814(a(n))) = A007949(a(n)),

%C - if a prime p > 3 divides a(n), then the p-adic valuation of a(n) belongs to this sequence.

%C Squarefree numbers coprime to 6 are in this sequence, and all members of this sequence are 0, 1, or 5 mod 6, so the lower density is at least 3/Pi^2 = 0.303... and the upper density is at most 1/2. This could be improved with more care. - _Charles R Greathouse IV_, May 17 2024

%e A300955(42) = 42 hence 42 belongs to this sequence.

%p b:= n-> `if`(n=1, 1, mul(`if`(i[1]=2, 3, `if`(i[1]=3,

%p 2, i[1]))^b(i[2]), i=ifactors(n)[2])):

%p select(n-> n=b(n), [$1..200])[]; # _Alois P. Heinz_, Mar 17 2018

%Y Cf. A007814, A007949, A279510, A300955.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Mar 17 2018