

A258456


Product of divisors of n is not a square.


1



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
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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_{dn} d is a prime.
If 1 + Product_{dn} d for n > 2 is a prime p, then Product_{dn} 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: A286972 A210994 A319237 * A230843 A188551 A045782
Adjacent sequences: A258453 A258454 A258455 * A258457 A258458 A258459


KEYWORD

nonn,easy


AUTHOR

Jaroslav Krizek, May 30 2015


STATUS

approved



