A258456 Product of divisors of n is not a square.

2, 3, 4, 5, 7, 9, 11, 12, 13, 17, 18, 19, 20, 23, 25, 28, 29, 31, 32, 36, 37, 41, 43, 44, 45, 47, 48, 49, 50, 52, 53, 59, 61, 63, 64, 67, 68, 71, 73, 75, 76, 79, 80, 83, 89, 92, 97, 98, 99, 100, 101, 103, 107, 109, 112, 113, 116, 117, 121, 124, 127, 131, 137

Offset

1,1

Comments

Numbers n such that A007955(n) is not a square.

Complement of A048943.

2 is only number n from this sequence such that 1 + Product_{d|n} d is a prime.

If 1 + Product_{d|n} d for n > 2 is a prime p, then Product_{d|n} d is a square (see A258455).

m is a term if and only if m is not a fourth power and the number of divisors of m is not a multiple of 4. - Chai Wah Wu, Mar 09 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

9 is in sequence because product of divisors of 9 = 1*3*9 = 27 is not square.

Mathematica

Select[Range@ 137, ! IntegerQ@ Sqrt[Times @@ Divisors@ #] &] (* Michael De Vlieger, Jun 02 2015 *)

Prog

(Magma) [n: n in [1..200] | not IsSquare(&*(Divisors(n)))]
(PARI) for(n=1, 100, d=divisors(n); p=prod(i=1, #d, d[i]); if(!issquare(p), print1(n, ", "))) \\ Derek Orr, Jun 12 2015
(Python)
from gmpy2 import iroot
from sympy import divisor_count
A258456_list = [i for i in range(1, 10**3) if not iroot(i, 4)[1] and divisor_count(i) % 4] # Chai Wah Wu, Mar 10 2016

Crossrefs

Cf. A007955, A118369, A118370, A258455.

Sequence in context: A331593 A319237 A331230 * A230843 A188551 A045782

Adjacent sequences: A258453 A258454 A258455 * A258457 A258458 A258459

Keyword

nonn,easy

Author

Jaroslav Krizek, May 30 2015

Status

approved