A329856 Numbers k such that usigma(uphi(k)) = k where usigma is the sum of unitary divisors of k (A034448) and uphi is the unitary totient function (A047994).

1, 3, 4, 5, 8, 9, 12, 17, 20, 24, 32, 36, 40, 68, 72, 96, 128, 136, 160, 257, 288, 384, 544, 640, 1028, 1152, 2056, 2176, 8192, 8224, 24576, 32896, 40960, 44352, 65537, 73728, 131072, 139264, 262148, 393216, 524288, 524296, 655360, 1179648, 1572864, 2097184

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..74 (terms below 5*10^10)

Example

3 is in the sequence since usigma(uphi(3)) = usigma(2) = 3.

Mathematica

usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); uphi[1] = 1; uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); Select[Range[10^4], usigma[uphi[#]] == # &]

Crossrefs

The unitary version of A018784.

Cf. A034448, A047994.

Sequence in context: A256173 A050070 A050590 * A327984 A066906 A125884

Adjacent sequences: A329853 A329854 A329855 * A329857 A329858 A329859

Keyword

nonn

Author

Amiram Eldar, Nov 22 2019

Status

approved