prog.sf

#!/usr/bin/ruby

# a(n) is the least integer k such that 1/(Sum_{j=0..n} 1/phi(k+j)) is an integer.
# https://oeis.org/A341799

# Known terms:
#   1, 3, 12, 13, 30, 31, 5654345764

# See also:
#   https://oeis.org/A341745

var n = 6
var range = (0..n)

Math.smooth_numbers(primes(71)...).each {|r|

    var k = 4680*r
    #var k = 379080*r

    if (k > 1e9) {

        (k+n).phi.is_smooth(100) || next

        if (range.all {|j| (k+j).phi.is_smooth(100) }) {
            say "Testing: #{k}"
            if (sum(0..n, {|j| phi(k+j).inv }).inv.is_int) {
                die "Found: #{k}"
            }
        }
    }
}

__END__

# For n = 4 (terms of A341745):

112123440
1231401600
9395357400
550424160000
1013280840000
8083217610000
53301680640000
65204622054000
442798714884240
448945897771800