Arithmetic derivative: Difference between revisions

=={{header|Julia}}==

<lang ruby>using Primes

D(n) = n < 0 ? -D(-n) : n < 2 ? zero(n) : isprime(n) ? one(n) : typeof(n)(sum(e * n ÷ p for (p, e) in eachfactor(n)))

foreach(p -> print(lpad(p[2], 5), p[1] % 10 == 0 ? "\n" : ""), pairs(map(D, -99:100)))

println()

for m in 1:20

println("D for 10^", rpad(m, 3), "divided by 7 is ", D(Int128(10)^m) ÷ 7)

end

</lang>{{out}}

<pre>

-75 -77 -1 -272 -24 -49 -34 -96 -20 -123

-1 -140 -32 -45 -22 -124 -1 -43 -108 -176

-1 -71 -18 -80 -55 -39 -1 -156 -1 -59

-26 -72 -1 -61 -18 -192 -51 -33 -1 -92

-1 -31 -22 -92 -16 -81 -1 -56 -20 -45

-14 -112 -1 -25 -39 -48 -1 -41 -1 -68

-16 -21 -1 -60 -12 -19 -14 -80 -1 -31

-1 -32 -27 -15 -10 -44 -1 -13 -10 -24

-1 -21 -1 -32 -8 -9 -1 -16 -1 -7

-6 -12 -1 -5 -1 -4 -1 -1 0 0

0 1 1 4 1 5 1 12 6 7

1 16 1 9 8 32 1 21 1 24

10 13 1 44 10 15 27 32 1 31

1 80 14 19 12 60 1 21 16 68

1 41 1 48 39 25 1 112 14 45

20 56 1 81 16 92 22 31 1 92

1 33 51 192 18 61 1 72 26 59

1 156 1 39 55 80 18 71 1 176

108 43 1 124 22 45 32 140 1 123

20 96 34 49 24 272 1 77 75 140

D for 10^1 divided by 7 is 1

D for 10^2 divided by 7 is 20

D for 10^3 divided by 7 is 300

D for 10^4 divided by 7 is 4000

D for 10^5 divided by 7 is 50000

D for 10^6 divided by 7 is 600000

D for 10^7 divided by 7 is 7000000

D for 10^8 divided by 7 is 80000000

D for 10^9 divided by 7 is 900000000

D for 10^10 divided by 7 is 10000000000

D for 10^11 divided by 7 is 110000000000

D for 10^12 divided by 7 is 1200000000000

D for 10^13 divided by 7 is 13000000000000

D for 10^14 divided by 7 is 140000000000000

D for 10^15 divided by 7 is 1500000000000000

D for 10^16 divided by 7 is 16000000000000000

D for 10^17 divided by 7 is 170000000000000000

D for 10^18 divided by 7 is 1800000000000000000

D for 10^19 divided by 7 is 19000000000000000000

D for 10^20 divided by 7 is 200000000000000000000

</pre>