OEIS A000028: Next term and membership test

Continuing our deep dive into A000028, the rule says a number n is in the sequence if the total number of 1s in the binary representations of the exponents in n's prime factorization is odd. The next term after 7 is 9: 8 = 2^3 has exponent 3 (binary 11) with two 1s (even), so 8 is out; 9 = 3^2 has exponent 2 (binary 10) with one 1, so 9 is in. We’ll walk through a quick check and reinforce why this pattern emerges.

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