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- #!/usr/bin/ruby
- # Generate the k-th power divisors of n.
- # See also:
- # https://oeis.org/A035316
- # https://oeis.org/A113061
- func power_divisors(n, k) {
- var d = [1]
- for p,e in (n.factor_exp) {
- e >= k || next
- d << gather {
- for j in (k..e `by` k) {
- take({|r| d.map {|u| u*r }...}(p**j))
- }
- }...
- }
- return d.sort
- }
- for n in (1..20) {
- say "2-power divisors of #{n} = #{power_divisors(n, 2)}"
- assert_eq(power_divisors(n, 2).len, 2.power_sigma0(n))
- assert_eq(power_divisors(n, 2).sum, 2.power_sigma(n))
- assert_eq(power_divisors(n, 3).len, 3.power_sigma0(n))
- assert_eq(power_divisors(n, 3).sum, 3.power_sigma(n))
- }
- __END__
- 2-power divisors of 1 = [1]
- 2-power divisors of 2 = [1]
- 2-power divisors of 3 = [1]
- 2-power divisors of 4 = [1, 4]
- 2-power divisors of 5 = [1]
- 2-power divisors of 6 = [1]
- 2-power divisors of 7 = [1]
- 2-power divisors of 8 = [1, 4]
- 2-power divisors of 9 = [1, 9]
- 2-power divisors of 10 = [1]
- 2-power divisors of 11 = [1]
- 2-power divisors of 12 = [1, 4]
- 2-power divisors of 13 = [1]
- 2-power divisors of 14 = [1]
- 2-power divisors of 15 = [1]
- 2-power divisors of 16 = [1, 4, 16]
- 2-power divisors of 17 = [1]
- 2-power divisors of 18 = [1, 9]
- 2-power divisors of 19 = [1]
- 2-power divisors of 20 = [1, 4]
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