prog.sf

#!/usr/bin/ruby

# Numbers that are both unitary and nonunitary harmonic numbers.
# https://oeis.org/A348923

# Known terms:
#   45, 60, 3780, 64260, 3112200, 6320160

# a(7) > 10^12, if it exists. - Amiram Eldar, Nov 04 2021

# Equivalently, numbers n such that usigma(n) divides n*usigma_0(n) and sigma(n) - usigma(n) divides n*(sigma_0(n) - usigma_0(n)).

# Non-squarefree numbers n such that A034448(n) divides n*A034444(n) and A048146(n) divides n*A048105(n).

# See also:
#   https://oeis.org/A247077

func isok(n) {
    imod(n*usigma0(n), usigma(n)) == 0 || return false
    imod(n*(sigma0(n) - usigma0(n)), sigma(n) - usigma(n)) == 0 || return false
    return true
}

assert([45, 60, 3780, 64260, 3112200, 6320160].all(isok))

Math.smooth_numbers(29.primes...).each {|n|
    say n if isok(n)
    #say n if (n > 1e12 && isok(n))
}