Faulhaber's formula supplies a functional-equation characterization of Bernoulli numbers that extends to closed-form expressions for power sums over half the totatives of n in terms of Dirichlet inverses of odd-degree Jordan totients.
Bernoulli number — Wikipedia, the free encyclopedia
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Faulhaber's formula, Bernoulli numbers, power sums of natural numbers and totatives and the functional equation $f(x)+x^k=f(x+1)$
Faulhaber's formula supplies a functional-equation characterization of Bernoulli numbers that extends to closed-form expressions for power sums over half the totatives of n in terms of Dirichlet inverses of odd-degree Jordan totients.