tl;dr Before 1975, two-thirds of senators "present and voting" were required for a supermajority, assuming a quorum is met (as few as 51 * (2/3) = 34 senators). After 1975, different percentages are required for different proposals. Two-thirds are needed for removal from office or rules changes (67 Senators normally), only three-fifths for cloture (60 Senators normally). Cloture doesn't count vacant seats, so if two senators are dead/removed (59 >= 98 * (3/5) = 58.8).
A supermajority is a requirement that more than a simple majority is needed to adopt a proposal. Since majorities and supermajorities are the minimum level of support required to adopt a proposal, you round up when finding the required number of Senators (normally 51 for a simple majority, 60 for a three-fifths supermajority, and 67 for a two-thirds supermajority).
A supermajority or a qualified majority is a requirement for a proposal to gain a specified greater level of support than a 50% simple majority.
Rule XXII allowed a supermajority for cloture to end debate. In 1975, the rules were modified from Senators "present and voting" to "duly chosen and sworn." This change was implement in 1975
"Is it the sense of the Senate that the debate shall be brought to a close?" And if that question shall be decided in the affirmative by three-fifths of the Senators duly chosen and sworn -- except on a measure or motion to amend the Senate rules, in which case the necessary affirmative vote shall be two-thirds of the Senators present and voting -- then said measure, motion, or other matter pending before the Senate, or the unfinished business, shall be the unfinished business to the exclusion of all other business until disposed of."
This change was invoked to make it easier to end debate in the Senate, and make filibustering weaker.
Filibusters were particularly useful to Southern senators who sought to block civil rights legislation, including anti-lynching legislation, until cloture was invoked after a 60 day filibuster against the Civil Right Act of 1964. In 1975, the Senate reduced the number of votes required for cloture from two-thirds to three-fifths, or 60 of the current one hundred senators.
Cloture votes don't count vacant seats when figuring 3/5ths, so you still need 60 with one vacancy, but only 59 with two vacancies (59 >= 98 * (3/5) = 58.8).
Invoking cloture usually requires a three-fifths vote of the entire Senate—“three-fifths of the Senators duly chosen and sworn.” Thus, if there is no more than one vacancy, 60 Senators must vote to invoke cloture. [...] Failing to vote on a cloture motion has the same effect as voting against the motion: it deprives the motion of one of the 60 votes needed to agree to it.