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Technical note proposes a formula to count Goldbach representations using kappa_1, indicating structural insights.
This technical note presents an exact formula for counting Goldbach representations using the function kappa_1. It introduces a normalized divisor profile theta_1, derived from kappa_1, which equals 1 exactly for prime numbers and is greater than 1 for composite numbers. A positive weighted sum is then defined from this profile, and its integer part is shown to recover exactly the number of non-ordered representations of an even integer as a sum of two primes. The result is structural rather than algorithmic and does not constitute a proof of Goldbach’s conjecture.
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Christophe POKORSKI (2026) studied this question.
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