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 A333171 a(n) = Sum_{k=0..n} d(k^2 + 1), where d(k) is the number of divisors of k (A000005). 1
 1, 3, 5, 9, 11, 15, 17, 23, 27, 31, 33, 37, 41, 49, 51, 55, 57, 65, 71, 75, 77, 85, 89, 97, 99, 103, 105, 113, 117, 121, 125, 133, 139, 147, 151, 155, 157, 165, 171, 175, 177, 183, 187, 199, 203, 207, 211, 227, 231, 235, 239, 243, 247, 255, 257, 265, 267, 283 (list; graph; refs; listen; history; text; internal format)
 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 Partial sums of A193432. Cf. A000005, A002522. Sequence in context: A268174 A166104 A164121 * A078651 A268732 A101114 Adjacent sequences: A333168 A333169 A333170 * A333172 A333173 A333174 KEYWORD nonn AUTHOR Amiram Eldar, Mar 09 2020 STATUS approved

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Last modified September 8 17:50 EDT 2024. Contains 375753 sequences. (Running on oeis4.)