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Square-free integers: Difference between revisions
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From 1 to 1000000 = 607926</pre>
=={{header|Maple}}==
<lang Maple>
with(NumberTheory):
with(ArrayTools):
squareFree := proc(n::integer)
if mul(PrimeFactors(n)) = n then return true;
else return false; end if;
return true;
end proc:
sfintegers := Array([]):
for count from 1 to 145 do
if squareFree(count) then Append(sfintegers, count); end if;
end do:
print(sfintegers):
sfintegers := Array([]):
for count from 10^12 to 10^12+145 do
if squareFree(count) then Append(sfintegers, count); end if;
end do:
print(sfintegers):
sfgroups := Array([]):
sfcount := 0:
for number from 1 to 100 do
if squareFree(number) then sfcount += 1: end if:
end do:
Append(sfgroups, sfcount):
for expon from 3 to 6 do
for number from 10^(expon - 1) to 10^expon do
if squareFree(number) then sfcount += 1: end if:
end do:
Append(sfgroups, sfcount):
end do:
seq(cat(sfgroups[i], " from 1 to ", 10^(i+1)), i = 1..5);
</lang>
{{out}}<pre>
[1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33,
34, 35, 37, 38, 39, 41, 42, 43, 46, 47, 51, 53, 55, 57, 58, 59, 61, 62, 65,
66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94,
95, 97, 101, 102, 103, 105, 106, 107, 109, 110, 111, 113, 114, 115, 118,
119, 122, 123, 127, 129, 130, 131, 133, 134, 137, 138, 139, 141, 142, 143,
145]
[1000000000001, 1000000000002, 1000000000003, 1000000000005, 1000000000006,
1000000000007, 1000000000009, 1000000000011, 1000000000013, 1000000000014,
1000000000015, 1000000000018, 1000000000019, 1000000000021, 1000000000022,
1000000000023, 1000000000027, 1000000000029, 1000000000030, 1000000000031,
1000000000033, 1000000000037, 1000000000038, 1000000000039, 1000000000041,
1000000000042, 1000000000043, 1000000000045, 1000000000046, 1000000000047,
1000000000049, 1000000000051, 1000000000054, 1000000000055, 1000000000057,
1000000000058, 1000000000059, 1000000000061, 1000000000063, 1000000000065,
1000000000066, 1000000000067, 1000000000069, 1000000000070, 1000000000073,
1000000000074, 1000000000077, 1000000000078, 1000000000079, 1000000000081,
1000000000082, 1000000000085, 1000000000086, 1000000000087, 1000000000090,
1000000000091, 1000000000093, 1000000000094, 1000000000095, 1000000000097,
1000000000099, 1000000000101, 1000000000102, 1000000000103, 1000000000105,
1000000000106, 1000000000109, 1000000000111, 1000000000113, 1000000000114,
1000000000115, 1000000000117, 1000000000118, 1000000000119, 1000000000121,
1000000000122, 1000000000123, 1000000000126, 1000000000127, 1000000000129,
1000000000130, 1000000000133, 1000000000135, 1000000000137, 1000000000138,
1000000000139, 1000000000141, 1000000000142, 1000000000145]
61 from 1 to 100, 608 from 1 to 1000, 6083 from 1 to 10000,
60794 from 1 to 100000, 607926 from 1 to 1000000
</pre>
=={{header|Mathematica}}==
<lang Mathematica>squareFree[n_Integer] := DeleteCases[Last /@ FactorInteger[n], 1] === {};
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