A122839 Numbers such that Sigma(m)*UnitarySigma(m)= k*UnitaryPhi(m)^2, for some integer k.

1, 2, 3, 6, 14, 15, 30, 35, 42, 60, 70, 78, 105, 190, 210, 312, 357, 418, 570, 714, 910, 1045, 1254, 1428, 2090, 2730, 3135, 3640, 4522, 4674, 5278, 6270, 10659, 10920, 12441, 13566, 14630, 15834, 16770, 18696, 20026, 21318, 23374, 24871, 24882, 24969, 25070, 25714, 27170

Offset: 1

Author

Yasutoshi Kohmoto, Oct 23 2006

Keywords

• nonn

Comments

Terms which are squarefree appear on A121556.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000203, A034448, A047994, A121556.

Programs

Maple

isA122839 := proc(m)
    A047994(m) ;
    modp(numtheory[sigma](m)*A034448(m),%^2) = 0 ;
end proc:
for m from 1 do
    if isA122839(m) then
        printf("%a,\n", m) ;
    end if;
end do: # R. J. Mathar, Sep 04 2018

Mathematica

f[p_, e_] := (p^(e+1)-1)*(p^e+1)/(p-1)/(p^e-1)^2; seqQ[1] = True; seqQ[n_] := IntegerQ [Times @@ (f @@@ FactorInteger[n])]; Select[Range[27170], seqQ] (* Amiram Eldar, Dec 11 2019 *)

PARI

isok(m) = ((sigma(m)*usigma(m)) % uphi(m)^2) == 0; \\ Michel Marcus, Jan 24 2019

Extensions

More terms from Michel Marcus, Jan 24 2019