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
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 29 2001
STATUS
approved