OFFSET
1,2
LINKS
Harry J. Smith and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (terms 1..500 from Smith)
EXAMPLE
MATHEMATICA
a[x_] := Abs[MoebiusMu[DivisorSigma[1, x]*EulerPhi[x]]] Do[s=as[n]; If[Equal[s, 1], Print[{n, Sqrt[n]}]], {n, 1, 1000000}]
Select[Range[250000], SquareFreeQ[DivisorSigma[1, #]*EulerPhi[#]]&] (* Harvey P. Dale, Jul 15 2015 *)
PROG
(PARI) n=0; for (m = 1, 10^9, s=abs(moebius(sigma(m)*eulerphi(m))); if (s==1, write("b065299.txt", n++, " ", m); if (n==500, return))) \\ Harry J. Smith, Oct 15 2009
(PARI) is(f)=my(n=#f~, v=List()); for(i=1, n, if(f[i, 1]>2, listput(v, f[i, 1]-1)); if(f[i, 2]>2, return(0), f[i, 2]>1, listput(v, f[i, 1])); listput(v, (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
sq(f)=f[, 2]*=2; f
double(f)=if(#f~ && f[1, 1]==2, f[1, 2]++, f=concat([2, 1], f)); f
list(lim)=my(v=List()); forsquarefree(n=1, sqrtint(lim\1), if(is(sq(n[2])), listput(v, n[1]^2))); forsquarefree(n=1, sqrtint(lim\2), if(is(double(sq(n[2]))), listput(v, 2*n[1]^2))); Set(v) \\ Charles R Greathouse IV, Feb 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 29 2001
STATUS
approved