Sublime number
Number that has a perfect number of factors adding up to another perfect number
title: "Sublime number" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["divisor-function", "integer-sequences"] description: "Number that has a perfect number of factors adding up to another perfect number" topic_path: "general/divisor-function" source: "https://en.wikipedia.org/wiki/Sublime_number" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Number that has a perfect number of factors adding up to another perfect number ::
In number theory, a sublime number is a positive integer which has a perfect number of positive factors (including itself), and whose positive factors add up to another perfect number.
The number 12, for example, is a sublime number. It has a perfect number of positive factors (6): 1, 2, 3, 4, 6, and 12, and the sum of these is again a perfect number: 1 + 2 + 3 + 4 + 6 + 12 = 28.
, there are only two known sublime numbers: 12 and (2126)(261 − 1)(231 − 1)(219 − 1)(27 − 1)(25 − 1)(23 − 1) . The second of these has 76 decimal digits: :6,086,555,670,238,378,989,670,371,734,243,169,622,657,830,773,351,885,970,528,324,860,512,791,691,264.
References
References
- MathPages article, [http://www.mathpages.com/home/kmath202/kmath202.htm "Sublime Numbers"].
- [[Clifford A. Pickover]], ''Wonders of Numbers, Adventures in Mathematics, Mind and Meaning'' New York: Oxford University Press (2003): 215
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