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- #!/usr/bin/ruby
- # Sum of exponential divisors (or e-divisors) of n.
- # Multiplicative with:
- # a(p^e, k) = Sum_{d|e} p^(d*k)
- # See also:
- # https://oeis.org/A051377
- func exponential_sigma(n, k=1) {
- n.factor_prod {|p,e|
- e.divisors.sum {|d| p**(d*k) }
- }
- }
- say map(1..20, {exponential_sigma(_, 1)})
- say map(1..20, {exponential_sigma(_, 2)})
- say map(1..20, {exponential_sigma(_, 3)})
- __END__
- [1, 2, 3, 6, 5, 6, 7, 10, 12, 10, 11, 18, 13, 14, 15, 22, 17, 24, 19, 30]
- [1, 4, 9, 20, 25, 36, 49, 68, 90, 100, 121, 180, 169, 196, 225, 276, 289, 360, 361, 500]
- [1, 8, 27, 72, 125, 216, 343, 520, 756, 1000, 1331, 1944, 2197, 2744, 3375, 4168, 4913, 6048, 6859, 9000]
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