cp's OEIS Frontend

A340675 Exponential of Mangoldt function conjugated by Tek's flip: a(n) = A225546(A014963(A225546(n))).

%I A340675 #29 Feb 07 2021 21:14:34
%S A340675 1,2,2,4,2,2,2,1,4,2,2,1,2,2,2,16,2,1,2,1,2,2,2,1,4,2,1,1,2,2,2,1,2,2,
%T A340675 2,4,2,2,2,1,2,2,2,1,1,2,2,1,4,1,2,1,2,1,2,1,2,2,2,1,2,2,1,1,2,2,2,1,
%U A340675 2,2,2,1,2,2,1,1,2,2,2,1,16,2,2,1,2,2,2,1,2,1,2,1,2,2,2,1,2,1,1,4,2,2,2,1,2
%N A340675 Exponential of Mangoldt function conjugated by Tek's flip: a(n) = A225546(A014963(A225546(n))).
%C A340675 Nonunit squarefree numbers take the value 2, other nonsquares take the value 1, and squares take the square of the value taken by their square root.
%H A340675 Antti Karttunen, <a href="/A340675/b340675.txt">Table of n, a(n) for n = 1..65537</a>
%H A340675 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%H A340675 <a href="/index/Pri#prime_signature">Index entries for sequences related to prime signature</a>
%F A340675 a(n) = A225546(A340673(n)) = A225546(A014963(A225546(n))).
%F A340675 a(n) = 2^A048298(A267116(n)).
%F A340675 If A340673(n) = 1, then a(n) = 1, otherwise a(n) = 2^A297108(A340673(n)).
%F A340675 If A340676(n) = 0, then a(n) = 1, otherwise a(n) = 2^(2^(A340676(n)-1)).
%F A340675 If n = s^(2^k), s squarefree >= 2, k >= 0, then a(n) = 2^(2^k), otherwise a(n) = 1.
%F A340675 For n, k > 1, if a(n) = a(k) then a(A331590(n, k)) = a(n), otherwise a(A331590(n, k)) = 1.
%F A340675 a(n^2) = a(n)^2.
%F A340675 a(A003961(n)) = a(n).
%F A340675 a(A051144(n)) = 1.
%F A340675 a(n) = 1 if and only if A331591(n) <> 1, otherwise a(n) = 2^A051903(n).
%o A340675 (PARI) A340675(n) = if(1==n,n,if(issquarefree(n), 2, if(!issquare(n), 1, A340675(sqrtint(n))^2)));
%Y A340675 Sequences used in a definition of this sequence: A014963, A048298, A225546, A267116, A297108, A340676.
%Y A340675 Cf. A051903, A051144, A331591, A340673.
%Y A340675 Positions of 1's: {1} U A340681, 2's: A005117 \ {1}, of 4's: A062503 \ {1}, of 16's: A113849.
%Y A340675 Positions of terms > 1: A340682, of terms > 2: A340674.
%Y A340675 Sequences used to express relationship between terms of this sequence: A003961, A331590.
%K A340675 nonn
%O A340675 1,2
%A A340675 _Antti Karttunen_ and _Peter Munn_, Feb 01 2021