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

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

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

Index entries for sequences computed from exponents in factorization of n

Index entries for sequences related to prime signature

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 * A356497 A097884 A094818

Adjacent sequences: A340672 A340673 A340674 * A340676 A340677 A340678

Keyword

nonn

Author

Antti Karttunen and Peter Munn, Feb 01 2021

Status

approved