Greatest prime dividing the n-th cubefree number: Difference between revisions
Greatest prime dividing the n-th cubefree number (view source)
Revision as of 16:39, 9 April 2024
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m (→resursive alternative: with max prime divisor for first 100. more compact.) |
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{{
;Definitions
A cubefree number is a positive integer whose prime factorization does not contain any third (or higher) power factors. If follows that all primes are trivially cubefree and the first cubefree number is 1 because it has no prime factors.
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The 1000000th term of a[n] is 1202057
The 10000000th term of a[n] is 1202057</pre>
=={{header|jq}}==
'''Works with jq, the C implementation of jq'''
'''Works with gojq, the Go implementation of jq'''
<syntaxhighlight lang="jq">
# The following may be omitted if using the C implementation of jq
def _nwise($n):
def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;
n;
### Generic functions
def lpad($len): tostring | ($len - length) as $l | (" " * $l) + .;
# tabular print
def tprint($columns; $width):
reduce _nwise($columns) as $row ("";
. + ($row|map(lpad($width)) | join(" ")) + "\n" );
# like while/2 but emit the final term rather than the first one
def whilst(cond; update):
def _whilst:
if cond then update | (., _whilst) else empty end;
_whilst;
## Prime factors
# Emit an array of the prime factors of 'n' in order using a wheel with basis [2, 3, 5]
# e.g. 44 | primeFactors => [2,2,11]
def primeFactors:
def out($i): until (.n % $i != 0; .factors += [$i] | .n = ((.n/$i)|floor) );
if . < 2 then []
else [4, 2, 4, 2, 4, 6, 2, 6] as $inc
| { n: .,
factors: [] }
| out(2)
| out(3)
| out(5)
| .k = 7
| .i = 0
| until(.k * .k > .n;
if .n % .k == 0
then .factors += [.k]
| .n = ((.n/.k)|floor)
else .k += $inc[.i]
| .i = ((.i + 1) % 8)
end)
| if .n > 1 then .factors += [ .n ] else . end
| .factors
end;
### Cube-free numbers
# If cubefree then emit the largest prime factor, else emit null
def cubefree:
if . % 8 == 0 or . % 27 == 0 then false
else primeFactors as $factors
| ($factors|length) as $n
| {i: 2, cubeFree: true}
| until (.cubeFree == false or .i >= $n;
$factors[.i-2] as $f
| if $f == $factors[.i-1] and $f == $factors[.i]
then .cubeFree = false
else .i += 1
end)
| if .cubeFree then $factors[-1] else null end
end;
## The tasks
{ res: [1], # by convention
count: 1, # see the previous line
i: 2,
lim1: 100,
lim2: 1000,
max: 10000 }
| whilst (.count <= .max;
.emit = null
| (.i|cubefree) as $result
| if $result
then .count += 1
| if .count <= .lim1 then .res += [$result] end
| if .count == .lim1
then .emit = ["First \(.lim1) terms of a[n]:"]
| .emit += [.res | tprint(10; 3)]
elif .count == .lim2
then .lim2 *= 10
| .emit = ["The \(.count) term of a[n] is \($result)"]
end
end
| .i += 1
| if .i % 8 == 0 or .i % 27 == 0
then .i += 1
end
)
| select(.emit) | .emit[]
</syntaxhighlight>
{{output}}
<pre>
First 100 terms of a[n]:
1 2 3 2 5 3 7 3 5 11
3 13 7 5 17 3 19 5 7 11
23 5 13 7 29 5 31 11 17 7
3 37 19 13 41 7 43 11 5 23
47 7 5 17 13 53 11 19 29 59
5 61 31 7 13 11 67 17 23 7
71 73 37 5 19 11 13 79 41 83
7 17 43 29 89 5 13 23 31 47
19 97 7 11 5 101 17 103 7 53
107 109 11 37 113 19 23 29 13 59
The 1000 term of a[n] is 109
The 10000 term of a[n] is 101
The 100000 term of a[n] is 1693
The 1000000 term of a[n] is 1202057
</pre>
=={{header|Julia}}==
| |||