A123041 Numbers m such that UnitarySigma(m)^2 = k*Sigma(m)*UnitaryPhi(m), for some integer k.
1, 2, 3, 6, 14, 15, 30, 35, 42, 70, 78, 105, 190, 210, 357, 418, 570, 714, 910, 1045, 1254, 1976, 2090, 2730, 3135, 4522, 4674, 5278, 5412, 5928, 6270, 8580, 10659, 12441, 12628, 13566, 14630, 15834, 16770, 17220, 20026, 21318, 23374, 24871, 24882
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..4309 (terms below 10^10; terms 1..1000 from Donovan Johnson)
Programs
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Mathematica
f[p_, e_] := (p - 1)*(p^e + 1)^2/((p^e - 1)*(p^(e + 1) - 1)); q[1] = True; q[n_] := IntegerQ[Times @@ f @@@ FactorInteger[n]]; Select[Range[25000], q] (* Amiram Eldar, Sep 12 2022 *)
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PARI
A047994(n)={ local(i,resul,rmax); if(n==1, return(1) ); i=factor(n); rmax=matsize(i)[1]; resul=1; for(r=1,rmax, resul *= i[r,1]^i[r,2]-1; ); return(resul); } A034448(n)={ sumdiv(n, d, if(gcd(d, n/d)==1, d)) } isA123041(n)={ local(s); s=(A034448(n))^2; if( s % (sigma(n)*A047994(n)) == 0, return(s/sigma(n)/A047994(n)), return(0) ); } { for(n=1,30000, k=isA123041(n); if( k, print1(n,",") ); ); } \\ R. J. Mathar, Sep 27 2006
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PARI
is(n) = {my(f=factor(n), p=f[,1], e=f[,2]); denominator(prod(i=1, #p, (p[i] - 1)*(p[i]^e[i] + 1)^2/((p[i]^e[i] - 1)*(p[i]^(e[i] + 1) - 1)))) == 1}; \\ Amiram Eldar, Sep 12 2022
Extensions
More terms from R. J. Mathar, Sep 27 2006
Comments