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

1,2

Comments

Terms which are squarefree appear on A121556.

Links

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

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 *)

Prog

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

Crossrefs

Cf. A000203, A034448, A047994, A121556.

Sequence in context: A134737 A030733 A335288 * A353869 A258077 A121556

Adjacent sequences: A122836 A122837 A122838 * A122840 A122841 A122842

Keyword

nonn

Author

Yasutoshi Kohmoto, Oct 23 2006

Extensions

More terms from Michel Marcus, Jan 24 2019

Status

approved