A300957 Fixed points of A300955.

1, 5, 6, 7, 11, 13, 17, 19, 23, 29, 30, 31, 35, 37, 41, 42, 43, 47, 53, 55, 59, 61, 65, 66, 67, 71, 72, 73, 77, 78, 79, 83, 85, 89, 91, 95, 97, 101, 102, 103, 107, 108, 109, 113, 114, 115, 119, 127, 131, 133, 137, 138, 139, 143, 145, 149, 151, 155, 157, 161

Offset: 1

Author

Rémy Sigrist, Mar 17 2018

Keywords

• nonn

Comments

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

For any n > 0:

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

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

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

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

Examples

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

Crossrefs

Cf. A007814, A007949, A279510, A300955.

Programs

Maple

b:= n-> `if`(n=1, 1, mul(`if`(i[1]=2, 3, `if`(i[1]=3,
             2, i[1]))^b(i[2]), i=ifactors(n)[2])):
select(n-> n=b(n), [$1..200])[]; # Alois P. Heinz, Mar 17 2018