OFFSET
0,2
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
Christopher Hooley, On the number of divisors of quadratic polynomials, Acta Mathematica, Vol. 110 (1963), pp. 97-114.
James McKee, On the average number of divisors of quadratic polynomials, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 117. No. 3 (1995), pp. 389-392, alternative link.
James McKee, The average number of divisors of an irreducible quadratic polynomial, Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 126. No. 1. (1999), pp. 17-22.
FORMULA
a(n) ~ (3/Pi) * n * log(n).
EXAMPLE
a(0) = d(0^1 + 1) = d(1) = 1.
a(1) = d(0^1 + 1) + d(1^1 + 1) = d(1) + d(2) = 1 + 2 = 3.
MATHEMATICA
Accumulate @ Table[DivisorSigma[0, k^2 + 1], {k, 0, 100}]
PROG
(PARI) a(n) = sum(k=0, n, numdiv(k^2+1)); \\ Michel Marcus, Mar 10 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 09 2020
STATUS
approved