Bateman, Paul T.; Grosswald, Emil On a theorem of Erdős and Szekeres. (English) Zbl 0079.07104 Ill. J. Math. 2, 88-98 (1958). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 ReviewsCited in 24 Documents Keywords:Number Theory PDF BibTeX XML Cite \textit{P. T. Bateman} and \textit{E. Grosswald}, Ill. J. Math. 2, 88--98 (1958; Zbl 0079.07104) Online Encyclopedia of Integer Sequences: Powerful numbers, definition (1): if a prime p divides n then p^2 must also divide n (also called squareful, square full, square-full or 2-powerful numbers). Number of powerful numbers <= 10^n. The number of cubefull numbers (A036966) not exceeding 10^n. Decimal expansion of Product_{p prime} (1 + 1/p^(4/3) + 1/p^(5/3)). Decimal expansion of zeta(3/4) * Product_{p prime} (1 + 1/p^(5/4) - 1/p^2 - 1/p^(9/4)) (negated). Decimal expansion of zeta(3/5) * zeta(4/5) * Product_{p prime} (1 - 1/p^(8/5) - 1/p^(9/5) - 1/p^2 + 1/p^(13/5) + 1/p^(14/5)).