A340673 If n is of the form s^(2^e), where s is a squarefree number, and e >= 0, then a(n) is the (1+e)-th prime, otherwise a(n) = 1.

1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 1, 2, 2, 2, 5, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 1, 3, 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, 5, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 3, 2, 2, 2, 1, 2

Offset: 1

Author

Antti Karttunen, Jan 31 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000040, A008578, A014963, A225546, A340675, A340676.

Positions of 1's: {1} U A340681, of 2's: A005117 \ {1}, of 3's: A062503 \ {1}, of 5's: A113849.

Positions of terms > 1: A340682, of terms > 2: A340674.

Programs

PARI

A008578(n) = if(1==n,n,prime(n-1));
A340673(n) = A008578(1+A340676(n)); \\ Uses also code from A340676.

Formula

a(n) = A014963(A225546(n)).

a(n) = A225546(A340675(n)).

a(n) = A008578(1+A340676(n)).

If n is of the form s^(2^e), where s is a squarefree number, and e >= 0, then a(n) = A000040(1+e), otherwise a(n) = 1.