A300957 - OEIS

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

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OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

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

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

CROSSREFS

Cf. A007814, A007949, A279510, A300955.

Sequence in context: A230995 A362929 A064615 * A139205 A374960 A288859

Adjacent sequences: A300954 A300955 A300956 * A300958 A300959 A300960

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Mar 17 2018

STATUS

approved