OEIS A00082: The n^2 × product over prime divisors (1+1/p) sequence — strong divisibility, multiplicativity, and links to zeta and modular forms

We dive into A00082, the sequence defined by A(n) = n^2 ∏_{p|n} (1 + 1/p). We'll see a concrete calculation (n = 12 gives A(12) = 288) and explore why it's a strong divisibility sequence, as well as why it's multiplicative. We’ll uncover connections to Dirichlet convolution with the Möbius function and the sum-of-squares function, and how the Dirichlet generating function ties to the Riemann zeta function. The episode surveys relations to related OEIS sequences (A181797, A003557, A0001615) and ideas like the sum of reciprocals (A335762) and asymptotic behavior involving π. We’ll also touch on the hinted link to elliptic modular functions and why A00082 sits at a fascinating crossroads in number theory.

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