A329730 Numbers k such that usigma(uphi(k)) = uphi(usigma(k)), where usigma is the sum of unitary divisors function (A034448) and uphi is the unitary totient function (A047994).

1, 3, 4, 8, 12, 24, 33, 91, 132, 201, 728, 812, 921, 1608, 1612, 2064, 2496, 2854, 3058, 3240, 3435, 3500, 4426, 5074, 5664, 5762, 6860, 7318, 7368, 8434, 9500, 9846, 10286, 11073, 12982, 13773, 14252, 14386, 17241, 17246, 18321, 18723, 18898, 19628, 21309, 21538

Offset

1,2

Comments

The unitary version of A033632.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

33 is the sequence since usigma(uphi(33)) = usigma(20) = 30 and uphi(usigma(33)) = uphi(48) = 30.

Mathematica

usigma[1]=1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); aQ[n_] := usigma[uphi[n]] == uphi[usigma[n]]; Select[Range[22000], aQ]

Crossrefs

Cf. A033632, A034448, A047994.

Sequence in context: A074331 A052952 A245121 * A153339 A275989 A343562

Adjacent sequences: A329727 A329728 A329729 * A329731 A329732 A329733

Keyword

nonn

Author

Amiram Eldar, Nov 19 2019

Status

approved