EPISODE · Sep 9, 2025 · 5 MIN
OEIS A000333: Partitions into non-integral powers
from Intellectually Curious · host Mike Breault
What happens when you count sums of square roots rather than sums of integers? OEIS A000333 counts the number of ordered multisets L = (l1 ≤ l2 ≤ … ≤ lk) of positive integers with sqrt(l1) + sqrt(l2) + … + sqrt(lk) ≤ n. For example, A(3) = 15. The problem arose in a 1951 statistical mechanics paper by Agarwala and Alok, where distributing energy quanta over non-integer energy levels led to these non-integral partitions; Neil Sloan later cataloged the sequence, highlighting its rapid growth (1, 5, 15, 40, 98, …) and the lack of a simple generating function, alongside intriguing asymptotic structure bridging number theory and physics.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.Sponsored by Embersilk LLC
Embed this episode
What this episode covers
What happens when you count sums of square roots rather than sums of integers? OEIS A000333 counts the number of ordered multisets L = (l1 ≤ l2 ≤ … ≤ lk) of positive integers with sqrt(l1) + sqrt(l2) + … + sqrt(lk) ≤ n. For example, A(3) = 15. The problem arose in a 1951 statistical mechanics paper by Agarwala and Alok, where distributing energy quanta over non-integer energy levels led to these non-integral partitions; Neil Sloan later cataloged the sequence, highlighting its rapid growth (1...
NOW PLAYING
OEIS A000333: Partitions into non-integral powers
No transcript for this episode yet
Similar Episodes
No similar episodes found.
Similar Podcasts
No similar podcasts found.