arithmetic_convolution.sf

#!/usr/bin/ruby

# Arithmetical convolution of two functions.

# See also:
#   https://en.wikipedia.org/wiki/Convolution

func convolution(n, f, g) {
    sum(1..n, {|k|
        f(k) * g(n - k + 1)
    })
}

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

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

say 20.of {|n| convolution(n, f, g) }     # https://oeis.org/A086733