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
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, May 30 2015
STATUS
approved