OEIS A000265: The largest odd divisor (the odd part of n)

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.

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