A362975 Decimal expansion of zeta(3/4) * Product_{p prime} (1 + 1/p^(5/4) - 1/p^2 - 1/p^(9/4)) (negated).

5, 8, 7, 2, 6, 1, 8, 8, 2, 0, 8, 1, 3, 8, 4, 2, 3, 9, 1, 0, 7, 4, 1, 3, 8, 1, 4, 2, 6, 6, 7, 8, 3, 5, 6, 1, 1, 4, 8, 6, 2, 6, 4, 3, 1, 1, 0, 8, 2, 9, 3, 5, 3, 5, 1, 7, 0, 7, 9, 8, 0, 4, 6, 6, 9, 0, 3, 9, 8, 2, 0, 5, 3, 5, 0, 1, 1, 2, 5, 3, 5, 6, 8, 6, 3, 3, 7, 5, 7, 9, 1, 7, 5, 1, 3, 0, 1, 2, 1, 3, 1, 6, 8, 4, 3

Offset: 1

Author

Amiram Eldar, May 11 2023

Keywords

• nonn
• cons

Comments

The coefficient c_1 of the second term in the asymptotic formula for the number of cubefull numbers (A036966) not exceeding x, N(x) = c_0 * x^(1/3) + c_1 * x^(1/4) + c_2 * x^(1/5) + o(x^(1/8)) (Bateman and Grosswald, 1958; Finch, 2003).

Examples

			-5.87261882081384239107413814266783561148626431108293...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, section 2.6.1, pp. 113-115.

Links

• Paul T. Bateman and Emil Grosswald, On a theorem of Erdős and Szekeres, Illinois Journal of Mathematics, Vol. 2, No. 1 (1958), pp. 88-98.
• P. Shiu, The distribution of cube-full numbers, Glasgow Mathematical Journal, Vol. 33, No. 3 (1991), pp. 287-295.
• P. Shiu, Cube-full numbers in short intervals, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 112, No. 1 (1992), pp. 1-5.

Crossrefs

Cf. A036966, A090699, A244000, A362973, A362974 (c_0), A362976 (c_2).

Programs

PARI

zeta(3/4) * prodeulerrat(1 + 1/p^5 - 1/p^8 - 1/p^9 ,1/4)