EPISODE · Jul 1, 2025 · 13 MIN
OEIS A000265: The largest odd divisor (the odd part of n)
from Intellectually Curious · host Mike Breault
In this Deep Dive, we explore A000265, the odd part of n obtained by removing all factors of 2. We explain the K·2^J decomposition (N = K·2^J with K odd), illustrate with examples, and show how A000265 is a multiplicative, strong-divisibility sequence. We'll reveal the fractal self-similarity inside the sequence, visualize its order with row-structures, and connect it to related OEIS entries like A07814. Finally, we discuss why isolating the odd part matters in number theory and how to compute A(n) from prime factorizations.Note: This podcast was AI-generated, and sometimes AI can make mistakes. Please double-check any critical information.Sponsored by Embersilk LLC
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In this Deep Dive, we explore A000265, the odd part of n obtained by removing all factors of 2. We explain the K·2^J decomposition (N = K·2^J with K odd), illustrate with examples, and show how A000265 is a multiplicative, strong-divisibility sequence. We'll reveal the fractal self-similarity inside the sequence, visualize its order with row-structures, and connect it to related OEIS entries like A07814. Finally, we discuss why isolating the odd part matters in number theory and how to comput...
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OEIS A000265: The largest odd divisor (the odd part of n)
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