cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A300957 Fixed points of A300955.

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%I A300957 #13 May 17 2024 09:55:53
%S A300957 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 A300957 67,71,72,73,77,78,79,83,85,89,91,95,97,101,102,103,107,108,109,113,
%U A300957 114,115,119,127,131,133,137,138,139,143,145,149,151,155,157,161
%N A300957 Fixed points of A300955.
%C A300957 For any n > 0, A279510(A279510(n)) belongs to this sequence (and this sequence is infinite).
%C A300957 For any n > 0:
%C A300957 - a(n) is a multiple of 2 iff a(n) is a multiple of 3,
%C A300957 - 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 A300957 - if a prime p > 3 divides a(n), then the p-adic valuation of a(n) belongs to this sequence.
%C A300957 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 A300957 A300955(42) = 42 hence 42 belongs to this sequence.
%p A300957 b:= n-> `if`(n=1, 1, mul(`if`(i[1]=2, 3, `if`(i[1]=3,
%p A300957              2, i[1]))^b(i[2]), i=ifactors(n)[2])):
%p A300957 select(n-> n=b(n), [$1..200])[]; # _Alois P. Heinz_, Mar 17 2018
%Y A300957 Cf. A007814, A007949, A279510, A300955.
%K A300957 nonn
%O A300957 1,2
%A A300957 _Rémy Sigrist_, Mar 17 2018