prog.sf

#!/usr/bin/ruby

# Number of distinct prime factors of sigma_n(n).
# https://oeis.org/A352420

include("../../../factordb/auto.sf")

func a(n) {
    var f = sigma_factors(n, n)
    #var f = sigma_factors_symbolic(n, n)
    f.map { FF_factordb(_) }.flat.uniq.len
}

for n in (1..1000) {
    #print(a(n), ", ")
    say "#{n} #{a(n)}"
}

__END__

# First 100 terms:

0, 1, 2, 3, 3, 4, 3, 2, 3, 5, 6, 8, 5, 5, 8, 6, 3, 8, 5, 11, 9, 7, 8, 10, 8, 8, 10, 12, 7, 13, 7, 11, 15, 10, 15, 11, 7, 8, 11, 10, 6, 14, 8, 14, 14, 11, 10, 17, 6, 21, 15, 16, 8, 18, 16, 15, 16, 6, 9, 22, 8, 10, 17, 13, 17, 17, 7, 17, 20, 17, 8, 23, 4, 13, 21, 16, 19, 21, 7, 22, 12, 8, 12, 29, 15, 8, 21, 15, 6, 32, 19, 16, 20, 12, 23, 26, 8, 19, 22, 32

a(67)-a(75) from ~~~~

# PARI/GP program:

a(n) = omega(sigma(n, n));