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A065303 Neither n nor sigma(n) is squarefree. 6
12, 24, 27, 28, 32, 40, 44, 48, 52, 54, 56, 60, 63, 68, 75, 76, 81, 84, 88, 90, 92, 96, 98, 99, 108, 112, 120, 124, 125, 126, 132, 135, 136, 140, 147, 150, 152, 153, 156, 160, 162, 164, 168, 171, 172, 175, 176, 184, 188, 189, 192, 198, 204, 207, 212, 216, 220 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

n = 147 = 3*7*7, sigma(147) = 2*2*3*19 = 228.

MATHEMATICA

Select[Range@ 220, Nor[SquareFreeQ@ #, SquareFreeQ@ DivisorSigma[1, #]] &] (* Michael De Vlieger, Mar 18 2017 *)

Select[Range[250], NoneTrue[{#, DivisorSigma[1, #]}, SquareFreeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 22 2019 *)

PROG

(PARI) n=0; for (m = 1, 10^9, if (!moebius(m) && !moebius(sigma(m)), write("b065303.txt", n++, " ", m); if (n==1000, return)) ) \\ Harry J. Smith, Oct 16 2009

(PARI) sigmaSquarefree(f)=my(v=vector(#f~, i, (f[i, 1]^(f[i, 2]+1)-1) / (f[i, 1]-1))); for(i=2, #v, for(j=1, i-1, if(gcd(v[i], v[j])>1, return(0)))); for(i=1, #v, if(!issquarefree(v[i]), return(0))); 1

list(lim)=my(v=List()); forfactored(k=12, lim\1, if(!issquarefree(k) && !sigmaSquarefree(k[2]), listput(v, k[1]))); Vec(v) \\ Charles R Greathouse IV, Jan 08 2018

(Python)

from sympy import divisor_sigma

from sympy.ntheory.factor_ import core

def is_squarefree(n): return core(n) == n

print([i for i in range(1, 251) if not is_squarefree(i) and not is_squarefree(divisor_sigma(i, 1))]) # Indranil Ghosh, Mar 18 2017

CROSSREFS

Cf. A000203, A008683, A065299, A065200, A065201, A065302.

Sequence in context: A095780 A119588 A167994 * A239673 A208158 A108902

Adjacent sequences:  A065300 A065301 A065302 * A065304 A065305 A065306

KEYWORD

nonn

AUTHOR

Labos Elemer, Oct 29 2001

STATUS

approved

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Last modified October 28 07:43 EDT 2021. Contains 348321 sequences. (Running on oeis4.)