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 A340675 Exponential of Mangoldt function conjugated by Tek's flip: a(n) = A225546(A014963(A225546(n))). 7
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = A225546(A340673(n)) = A225546(A014963(A225546(n))). a(n) = 2^A048298(A267116(n)). If A340673(n) = 1, then a(n) = 1, otherwise a(n) = 2^A297108(A340673(n)). If A340676(n) = 0, then a(n) = 1, otherwise a(n) = 2^(2^(A340676(n)-1)). If n = s^(2^k), s squarefree >= 2, k >= 0, then a(n) = 2^(2^k), otherwise a(n) = 1. For n, k > 1, if a(n) = a(k) then a(A331590(n, k)) = a(n), otherwise a(A331590(n, k)) = 1. a(n^2) = a(n)^2. a(A003961(n)) = a(n). a(A051144(n)) = 1. a(n) = 1 if and only if A331591(n) <> 1, otherwise a(n) = 2^A051903(n). PROG (PARI) A340675(n) = if(1==n, n, if(issquarefree(n), 2, if(!issquare(n), 1, A340675(sqrtint(n))^2))); CROSSREFS Sequences used in a definition of this sequence: A014963, A048298, A225546, A267116, A297108, A340676. Cf. A051903, A051144, A331591, A340673. Positions of 1's: {1} U A340681, 2's: A005117 \ {1}, of 4's: A062503 \ {1}, of 16's: A113849. Positions of terms > 1: A340682, of terms > 2: A340674. Sequences used to express relationship between terms of this sequence: A003961, A331590. Sequence in context: A239675 A289827 A092188 * A097884 A094818 A114233 Adjacent sequences:  A340672 A340673 A340674 * A340676 A340677 A340678 KEYWORD nonn AUTHOR Antti Karttunen and Peter Munn, Feb 01 2021 STATUS approved

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Last modified September 18 01:39 EDT 2021. Contains 347504 sequences. (Running on oeis4.)