A381605 Number of distinct prime divisors of n^3+1.
1, 1, 2, 2, 3, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 4, 2, 3, 3, 3, 2, 3, 3, 3, 3, 4, 2, 4, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 4, 2, 4, 3, 4, 3, 4, 3, 4, 4, 3, 3, 3, 4, 3, 4, 4, 2, 5, 2, 4, 4, 2, 4, 5, 3, 3, 4, 5, 2, 3, 2, 4, 3, 5, 3, 4, 2, 3, 3, 3, 4, 4, 4, 4, 3, 4, 4, 5, 3, 3, 3, 4, 4, 4, 3, 4, 3, 4, 2
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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MATLAB
function result = a(n) result = numel(unique(factor(sym(n^3+1)))); end
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Maple
f:= proc(n) nops(numtheory:-factorset(n^3+1)) end proc: map(f, [$1..50]); # Robert Israel, Apr 03 2025
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Mathematica
Table[PrimeNu[n^3 + 1], {n, 1, 30}] -
PARI
a(n) = omega(n^3+1); \\ Michel Marcus, Mar 01 2025
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PARI
a(n)=if(n%3==2, omega((n+1)/3^valuation(n+1,3)) + omega((n^2-n+1)/3^valuation(n^2-n+1,3)) + 1, omega(n+1) + omega(n^2-n+1)) \\ Charles R Greathouse IV, Mar 03 2025
Formula
a(n) > 1 for n > 2. - Charles R Greathouse IV, Mar 03 2025