sidef-scripts/Math/dirichlet_convolution.sf

#!/usr/bin/ruby

# Dirichlet convolution of two functions.

# See also:
#   https://oeis.org/wiki/Dirichlet_convolution
#   https://en.wikipedia.org/wiki/Dirichlet_convolution

func dirichlet_convolution(n, f, g) {
    n.divisor_sum {|d|
        f(d) * g(n/d)
    }
}

# Example:
#   Dirichlet convolution of sigma(n) (A000203) with phi(n) (A000010).

var f = { .sigma }
var g = { .euler_phi }

say 20.of {|n| dirichlet_convolution(n, f, g) }     # https://oeis.org/A038040