This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383672 #17 May 09 2025 19:59:59 %S A383672 7,38,41,43,57,70,82,93,107,118,143,157,182,193,218,239,251,257,282, %T A383672 293,307,318,327,357,382,393,407,418,437,443,457,482,493,515,518,543, %U A383672 557,577,582,593,606,607,618,643,682,707,718,743,746,757,782,793,807,818,829,843,857,893 %N A383672 Squarefree numbers k such that k^2+1 is not squarefree. %e A383672 38 = 2*19 is squarefree but 38*38 + 1 = 1445 = 5*17*17 is not squarefree. %p A383672 filter:= proc(n) numtheory:-issqrfree(n) and not numtheory:-issqrfree(n^2+1) end proc: %p A383672 select(filter, [$1..1000]); # _Robert Israel_, May 04 2025 %t A383672 Select[Range[900],SquareFreeQ[#] && !SquareFreeQ[#^2+1] &] (* _Stefano Spezia_, May 04 2025 *) %o A383672 (Python) %o A383672 from sympy import factorint %o A383672 def is_squarefree(n): %o A383672 return all(exponent == 1 for exponent in factorint(n).values()) %o A383672 print([a for a in range(1,900) if is_squarefree(a) and not(is_squarefree(a*a + 1))]) %o A383672 (PARI) isok(k) = issquarefree(k) && !issquarefree(k^2+1); \\ _Michel Marcus_, May 04 2025 %Y A383672 Intersection of A005117 and A049532. %Y A383672 Includes A141932 and A141941. %Y A383672 Cf. A080666, A224718. %K A383672 nonn %O A383672 1,1 %A A383672 _Alexandre Herrera_, May 04 2025