Part of the answer can be found in this passage from Drake's chapter, "The Foundations of the Voyager Record," in Murmurs of Earth, a popular book edited by Carl Sagan which came out at around the time of the Voyager launchings:
"About this time [1961] Lingua Cosmica, a book on interstellar
codes, was published by Hans Freudenthal, a Yale mathematician. It
contained an ingenious method to construct a language by utilizing
simple mathematics to establish simple rules and concepts. For
example, an equation such as $2+3=5$ and another equation such as
$4+5=9$ can be used to establish the meaning of the plus sign and the
equal sign.... Freudenthal showed that by using such
mathematical equations one could develop quite a sophisticated
language -- in fact even an ability in the end to express emotion."
The book by Freudenthal that Drakes cites is actually titled Lincos: Design of a Language for Cosmic Intercourse Part I. ("Lincos" is a contraction of "Lingua Cosmica.") Freudenthal's book is in the tradition of Russell and Whitehead's Principia Mathematica, with pages and pages of logical impenetralia. There is no Part II.
Incidentally, there is a fun 1961 essay, Extraterrestrial Linguistics, by Solomon Golomb of polyomino fame. Here's an excerpt (with an interpolated "[more]" to make sense of one of the sentences):
"[I]t is probably rank terrestrial provincialism to expect others to
attach the same importance to pi that we do. Even in our own
mathematics, such constants as e and log 2 are considered [more]
important, and the exaggerated role of pi stems largely from the
Greeks' undue efforts attempting to square the circle....
"My own recommendation is the prime sequence $2, 3, 5, 7, 11, 13, 17, 19, 23,\ldots$, with a long period to prove the non-accidental nature
of the signal. It isn't so much that I'm sure these
Extra-terrestrials would recognize the primes; but if they don't,
they must be dull fellows, and I would just as soon uot [sic] get
acquainted."
