A333167 a(n) = r_2(n^2 + 1), where r_2(k) is the number of ways of writing k as a sum of 2 squares (A004018).

4, 4, 8, 8, 8, 8, 8, 12, 16, 8, 8, 8, 16, 16, 8, 8, 8, 16, 24, 8, 8, 16, 16, 16, 8, 8, 8, 16, 16, 8, 16, 16, 24, 16, 16, 8, 8, 16, 24, 8, 8, 12, 16, 24, 16, 8, 16, 32, 16, 8, 16, 8, 16, 16, 8, 16, 8, 32, 16, 8, 16, 8, 16, 16, 16, 8, 8, 16, 32, 8, 24, 8, 32, 32

Offset

0,1

References

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 166.

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

E. J. Scourfield, The divisors of a quadratic polynomial, Glasgow Mathematical Journal, Vol. 5, No. 1 (1961), pp. 8-20.

Formula

a(n) = A004018(A002522(n)).

Example

a(0) = r_2(0^2 + 1) = r_2(1) = A004018(1) = 4.

Mathematica

Table[SquaresR[2, k^2 + 1], {k, 0, 100}]

Crossrefs

Cf. A004018, A002522, A193432, A193433, A333169.

Sequence in context: A264606 A016712 A346062 * A246066 A076359 A105675

Adjacent sequences: A333164 A333165 A333166 * A333168 A333169 A333170

Keyword

nonn

Author

Amiram Eldar, Mar 09 2020

Status

approved