sum_of_nth_power_digits.sf

#!/usr/bin/ruby

# Generate all the numbers that can be written as the sum of n-th powers of their digits.

# OEIS sequences:
#   https://oeis.org/A005188 -- Armstrong (or pluperfect, or Plus Perfect, or narcissistic) numbers: m-digit positive numbers equal to sum of the m-th powers of their digits.
#   https://oeis.org/A252648 -- Irregular table of perfect digital invariants for n > 1, i.e., numbers equal to the sum of n-th powers of their digits, read by rows.

# See also:
#   https://projecteuler.net/problem=30
#   https://rosettacode.org/wiki/Digit_fifth_powers

func digit_nth_powers(n, base=10) {

    var D = @(^base)
    var P = D.map {|d| d**n }
    var A = []
    var m = (base-1)**n

    for(var (k, t) = (1, 1); k*m >= t; (++k, t*=base)) {
        D.combinations_with_repetition(k, {|*c|
            var v = c.sum {|d| P[d] }
            A.push(v) if (v.digits(base).sort == c)
        })
    }

    A.sort.grep { _ > 1 }
}

for n in (3..5) {
    var a = digit_nth_powers(n)
    say "Sum of #{n}-th powers of their digits: #{a}"
}

__END__
Sum of 3-th powers of their digits: [153, 370, 371, 407]
Sum of 4-th powers of their digits: [1634, 8208, 9474]
Sum of 5-th powers of their digits: [4150, 4151, 54748, 92727, 93084, 194979]
Sum of 6-th powers of their digits: [548834]
Sum of 7-th powers of their digits: [1741725, 4210818, 9800817, 9926315, 14459929]
Sum of 8-th powers of their digits: [24678050, 24678051, 88593477]