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- #!/usr/bin/ruby
- # Numbers that are both infinitary and noninfinitary harmonic numbers
- # https://oeis.org/A348922
- # Known terms:
- # 45, 60, 54600, 257040, 1801800, 2789640, 4299750, 47297250, 1707259680, 4093362000
- # a(7) > 10^10, if it exists. - Amiram Eldar, Nov 04 2021
- # Equivalently, numbers n such that isigma(n) divides n*isigma_0(n) and nisigma(n) divides n*nisigma_0(n).
- # Non-squarefree numbers n such that A049417(n) divides n*A037445(n) and A348271(n) divides n*A348341(n).
- # See also:
- # https://oeis.org/A247077
- func isok(n) {
- imod(n*isigma0(n), isigma(n)) == 0 || return false
- imod(n*nisigma0(n), nisigma(n)) == 0 || return false
- return true
- }
- assert([45, 60, 54600, 257040, 1801800, 2789640, 4299750, 47297250, 1707259680, 4093362000].all(isok))
- Math.smooth_numbers(41.primes...).each {|n|
- say n if isok(n)
- #say n if (n > 1e12 && isok(n))
- }
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