A329855 Numbers k such that uphi(usigma(k)) = k where usigma is the sum of unitary divisors of k (A034448) and uphi is the unitary totient function (A047994).

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 24, 28, 31, 48, 56, 62, 112, 124, 127, 248, 254, 256, 496, 508, 768, 1016, 1792, 2032, 7936, 8191, 16382, 30240, 32512, 32764, 65528, 65536, 131056, 131071, 196608, 262142, 458752, 524284, 524287, 1048568, 1048574, 2031616

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 uphi(usigma(3)) = uphi(4) = 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], uphi[usigma[#]] == # &]

Crossrefs

The unitary version of A001229.

Cf. A034448, A047994.

Sequence in context: A054784 A018585 A018399 * A029748 A018314 A212216

Adjacent sequences: A329852 A329853 A329854 * A329856 A329857 A329858

Keyword

nonn

Author

Amiram Eldar, Nov 22 2019

Status

approved