A348601 Nonexponential multiply-perfect numbers: numbers k such that k | A160135(k).

1, 6, 40, 234, 588, 89376, 10805558400

Offset

1,2

Comments

The corresponding quotients A160135(k)/k are 1, 1, 1, 1, 1, 2, 3, ...

a(8) > 1.5*10^10, if it exists.

Links

Table of n, a(n) for n=1..7.

Example

6 is a term since its nonexponential divisors are 1, 2 and 3, so A160135(6) = 1 + 2 + 3 = 6 which is divisible by 6.
40 is a term since its nonexponential divisors are 1, 2, 4, 5, 8 and 20, so A160135(40) = 1 + 2 + 4 + 5 + 8 + 20 = 40 which is divisible by 40.

Mathematica

esigma[n_] := Times @@ (Sum[First[#]^d, {d, Divisors[Last[#]]}] &) /@ FactorInteger[n]; Select[Range[1000], Divisible[DivisorSigma[1, #] - esigma[#], #] &]

Crossrefs

Cf. A160135.

Similar sequences: A007691, A064594, A064595, A189000, A327158.

Sequence in context: A229580 A254945 A026077 * A065113 A052518 A135032

Adjacent sequences: A348598 A348599 A348600 * A348602 A348603 A348604

Keyword

nonn,more

Author

Amiram Eldar, Oct 25 2021

Status

approved