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A065303 Neither n nor sigma(n) is squarefree.

%I A065303 #28 May 16 2020 03:34:27
%S A065303 12,24,27,28,32,40,44,48,52,54,56,60,63,68,75,76,81,84,88,90,92,96,98,
%T A065303 99,108,112,120,124,125,126,132,135,136,140,147,150,152,153,156,160,
%U A065303 162,164,168,171,172,175,176,184,188,189,192,198,204,207,212,216,220
%N A065303 Neither n nor sigma(n) is squarefree.
%H A065303 Harry J. Smith, <a href="/A065303/b065303.txt">Table of n, a(n) for n = 1..1000</a>
%e A065303 n = 147 = 3*7*7, sigma(147) = 2*2*3*19 = 228.
%t A065303 Select[Range@ 220, Nor[SquareFreeQ@ #, SquareFreeQ@ DivisorSigma[1, #]] &] (* _Michael De Vlieger_, Mar 18 2017 *)
%t A065303 Select[Range[250],NoneTrue[{#,DivisorSigma[1,#]},SquareFreeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 22 2019 *)
%o A065303 (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
%o A065303 (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
%o A065303 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
%o A065303 (Python)
%o A065303 from sympy import divisor_sigma
%o A065303 from sympy.ntheory.factor_ import core
%o A065303 def is_squarefree(n): return core(n) == n
%o A065303 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
%Y A065303 Cf. A000203, A008683, A065299, A065200, A065201, A065302.
%K A065303 nonn
%O A065303 1,1
%A A065303 _Labos Elemer_, Oct 29 2001