A353471 a(n) = 1 if n is a prime or a squarefree semiprime, otherwise 0.

0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0

Offset

1

Comments

a(n) = 1 if the number of the divisors of n, tau(n), is equal to the twice number of distinct prime factors of n, 2*omega(n), otherwise 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A010051(n) + A280710(n).

a(n) = [A000005(n) == 2*A001221(n)], where [ ] is the Iverson bracket.

Prog

(PARI) A353471(n) = (numdiv(n)==2*omega(n));

Crossrefs

Characteristic function of A167171, the union of primes (A000040) and squarefree semiprimes (A006881).

Cf. A000005, A001221, A010051, A280710.

Sequence in context: A323153 A288861 A030190 * A157658 A296211 A341642

Adjacent sequences: A353468 A353469 A353470 * A353472 A353473 A353474

Keyword

nonn

Author

Antti Karttunen, Apr 21 2022

Status

approved