experimental-projects/oeis-research/Daniel Suteu/Smallest Carmichael number such that gpf(p-1) = prime(n)/prog.sf

#!/usr/bin/ruby

# a(n) is the smallest Carmichael number such that gpf(p-1) = prime(n) for all prime factors p of a(n), or 0 if no such number exists.

# a(2) = 1729
# a(3) = 252601
# a(4) = 1152271
# a(5) = 1615681
# a(6) = 4335241
# a(7) = 172947529

# Lower bound for n > 2:
#   a(n) >= (2*p + 1)*(2*3*p + 1)*(2*7*p + 1), where p = prime(n).

func a(n) {
    var p = prime(n)
    var from = (2*p + 1)*(2*3*p + 1)*(2*7*p + 1)
    from = 1 if(n == 2)
    from..Inf -> first {|k|
        k.is_composite && k.is_carmichael && k.factor.all { .dec.gpf == p }
    }
}

for n in (2..10) {
    say ("a(#{n}) = ", a(n))
}