(Source: Ritter 1980 Kakteen in Sudamerika Volume 2)

  The name Trichocereus andalgalensis appeared twice in the literature.

  Trichocereus andalgalensis (Weber) Kreuzinger (1935: Verzeichnis Sukkulenten mit Revision Syst. Kakt., S. 36)
   and
  Trichocereus andalgalensis (Weber) Hosseus (1939: Notas s. Cact. argent.)

Originally described as Cereus andalgalensis Weber (1898: in Schumann's Gesamtbeschr. Kakt., S. 151)
Said by Weber to occur in two varieties:
  var. flaviflorus (yellow flowers)
   and
  var. rubriflorus (red flowers)

Ritter considered Cereus andalgalensis var. rubriflorus to be a synonym of
Trichocereus andalgalensis (Weber) Kreuringer
  and
Cereus andalgalensis var. rubriflorus Weber to be a synonym of
Trichocereus huascha (Weber) Ritter (non Britton & Rose 1920; non Werdermann 1933)

Helianthocereus andalgalensis (Weber) Backeberg
  and
Helianthocereus huascha var. rubriflorus (Weber) Backeberg
were both refered to Trichocereus huascha by Ritter.

Trichocereus andalgalensis var. auricolor
was proposed by Ritter (1980:2:438) as a new name for the combination of
  Trichocereus auricolor Backeberg (1935: Backeberg & Knuth's Kaktus-ABC)
  and
  Helianthocereus huascha (Weber) Backberg var. auricolor (Backeberg) Backeberg

Photo of Trichocereus andalgalensis var. auricolor flowering (B&W) page 795: plate 560.

Echinopsis synonymy:
According to Hunt 1999 CITES Cactaceae Checklist:

  Does not mention either Echinopsis andalgalensis OR Trichocereus andalgalensis
  Dismisses Lobivia andalgalensis (Weber ex Schumann) Britton & Rose
as a synonym of Echinopsis huascha (Weber) Friedrich & Rowley. (p. 71)