A228409 a(n) = 4*mu(n) + 5, where mu is the Moebius function (A008683).

9, 1, 1, 5, 1, 9, 1, 5, 5, 9, 1, 5, 1, 9, 9, 5, 1, 5, 1, 5, 9, 9, 1, 5, 5, 9, 5, 5, 1, 1, 1, 5, 9, 9, 9, 5, 1, 9, 9, 5, 1, 1, 1, 5, 5, 9, 1, 5, 5, 5, 9, 5, 1, 5, 9, 5, 9, 9, 1, 5, 1, 9, 5, 5, 9, 1, 1, 5, 9, 1, 1, 5, 1, 9, 5, 5, 9, 1, 1, 5, 5, 9, 1, 5, 9, 9, 9

Offset

1,1

Comments

If n is prime (A000040), then a(n) = 1. The converse is not true: when n is the product of an odd number of distinct primes, mu(n) = -1 => a(n) = 1 (30 = 2*3*5, so a(30) = 1).

If n is semiprime (A001358), a(n) gives the number of divisors of n^2. In particular, if n = p^2 then n^2 = (p^2)^2 = p^4 has 5 divisors: p^4, p^3, p^2, p, 1. If n = pq (p,q distinct primes) then n^2 = (pq)^2 has 9 divisors: (pq)^2, qp^2, pq^2, p^2, q^2, pq, p, q, and 1.

a(n) = 1 if and only if n has an odd number of distinct prime factors, A030059. - Jon Perry, Nov 12 2013.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

Example

a(6) = 9; 4*mu(6) + 5 = 4*1 + 5 = 9.

Maple

with(numtheory); A228409:=n->4*mobius(n)+5; seq(A228409(n), n=1..100);

Mathematica

Table[4 MoebiusMu[n] + 5, {n, 100}]

Prog

(PARI) a(n)=4*moebius(n)+5 \\ Charles R Greathouse IV, Nov 12 2013
(Scheme) (define (A228409 n) (+ 5 (* 4 (A008683 n)))) ;; Antti Karttunen, Jul 26 2017

Crossrefs

Cf. A000040, A001358, A008683, A030059.

Sequence in context: A037478 A198551 A010162 * A230155 A072224 A296547

Adjacent sequences: A228406 A228407 A228408 * A228410 A228411 A228412

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Nov 09 2013

Status

approved