A379350 -id:A379350 - cp's OEIS frontend

A379351 a(n) is the greatest prime factor of n^2 + 2.

2, 3, 3, 11, 3, 3, 19, 17, 11, 83, 17, 41, 73, 19, 11, 227, 43, 97, 163, 11, 67, 443, 3, 59, 17, 19, 113, 43, 131, 281, 41, 107, 19, 1091, 193, 409, 59, 457, 241, 1523, 89, 17, 883, 617, 19, 2027, 353, 67, 1153, 89, 139, 137, 41, 937, 1459, 1009, 523, 3251, 17, 43, 1801

Offset: 0

Andrew Howroyd, Dec 22 2024

nonn

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A006530, A059100, A379350.

FactorInteger[#][[-1,1]]&/@(Range[0,60]^2+2) (* Harvey P. Dale, Dec 31 2024 *)

PARI
```
a(n) = {vecmax(factor(n^2 + 2)[,1])}
```

a(n) = A006530(A059100(n)).

A379349 Number of integers of the form k^2 + 2 whose greatest prime factor is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.

Original entry on oeis.org

1, 5, 5, 7, 11, 12, 18, 18, 21, 25, 30, 47, 39, 45, 62, 63, 83, 81, 107, 105, 130

Offset: 1

Andrew Howroyd, Dec 22 2024

See A379350 for additional information.

			Table showing n, p = A033203(n) and a(n):
   1    2    1
   2    3    5
   3   11    5
   4   17    7
   5   19   11
   6   41   12
   7   43   18
   8   59   18
   9   67   21
  10   73   25
  ...

Filip Najman, Smooth values of some quadratic polynomials, Glasnik Matematicki Series III 45 (2010), pp. 347-355.

Row lengths of A379350.

Cf. A033203, A181471, A379346, A379348.

A379352 a(n) is the smallest nonnegative integer k such the greatest prime factor of k^2 + 2 is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.

Original entry on oeis.org

0, 1, 3, 7, 6, 11, 16, 23, 20, 12, 9, 40, 17, 31, 26, 28, 51, 50, 18, 78, 34, 93, 15, 109, 38, 91, 68, 29, 127, 108, 130, 75, 141, 107, 46, 120, 143, 35, 96, 69, 21, 214, 37, 126, 94, 67, 163, 56, 190, 261, 216, 153, 239, 207, 260, 104, 43, 288, 62, 206, 77, 262, 64, 151, 346

Offset: 1

Andrew Howroyd, Dec 22 2024

nonn

			Table showing n, A033203(n), a(n), a(n)^2 + 2:
   1  2  0   2
   2  3  1   3
   3 11  3  11
   4 17  7  51 = 17*3
   5 19  6  38 = 19*2
   6 41 11 123 = 41*3
   7 43 16 258 = 43*3*2
   8 59 23 531 = 59*3^2
   9 67 20 402 = 67*3*2
  10 73 12 146 = 73*2
  ...

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Cf. A033203, A059100, A006530, A185397, A379350, A379351.

lista(n) = { my(L=List(),p=0); while(#L5&&r<>7, my(k=0); while(vecmax(factor(k^2 + 2)[,1]) <> p, k++); listput(L,k) )); Vec(L) }

cp's OEIS Frontend

A379351 a(n) is the greatest prime factor of n^2 + 2.

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A379349 Number of integers of the form k^2 + 2 whose greatest prime factor is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.

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A379352 a(n) is the smallest nonnegative integer k such the greatest prime factor of k^2 + 2 is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.

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Author

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PARI