Untouchable numbers: Difference between revisions

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spds=:([:sum_of_proper_divisors"0(#\@i.-.i.&.:(p:inv))@*:)f. NB. remove primes which contribute 1

</lang>

We may revisit to correct the larger untouchable tallies. J ~~is an algorithm description language. The~~ algorithm presented is ~~straightforward and~~ a little bit efficient, and, I claim, the verb <tt>(candidates-.spds)</tt> produces the full list of untouchable numbers up to its argument. It considers the sum of proper divisors through the argument squared, less primes.

We may revisit to correct the larger untouchable tallies. The straightforward algorithm presented is a little bit efficient, and, I claim, the verb <tt>(candidates-.spds)</tt> produces the full list of untouchable numbers up to its argument. It considers the sum of proper divisors through the argument squared, less primes. Since J is an algorithm description language, it may be "fairer" to state in J that "more resources required" than in some other language. [https://www.eecg.utoronto.ca/~jzhu/csc326/readings/iverson.pdf]

Time (seconds) and space (bytes) on a high end six year old (new in 2015) laptop computer.

<pre>

timespacex'(-.candidates@#)/:~~.spds 10000'

600.285 4.29497e9

</pre>

<pre>

UNTOUCHABLES=:(candidates-.spds) 2000 NB. compute untouchable numbers

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1884 1888 1894 1896 1920 1922 1944 1956 1958 1960 1962 1972 1986 1992

SBD=:spds 10000 NB. sums of proper divisors of many integers

T=:/:~~.SBD NB. sort the nub

#T NB. leaving this many touchable numbers, which are dense through at least 10000

47269787

U=:(-.~candidates@#)T NB. possible untouchable numbers

head=: ~~(<;._1~~~ ';'~~&=)';n;~~tally of possible untouchable numbers to n'

head=: 'n';'tally of possible untouchable numbers to n'

head,:,.L:0;/|:(,.U&I.)10^#\i.5 NB. testing to ten thousand squared

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