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 A160114 Fluctuations of the number of cubefree integers not exceeding 10^n 1
 0, 1, 2, 1, 0, -1, 3, 7, -10, -1, -7, -14, -59, 21, 34, -15, 103, -104, 302, -38, -514, -290, 1130, 504, 2466, 6813, -1854, 1590, -4879, 3963 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The asymptotic density of cubefree integers is the reciprocal of Apery's constant 1/zeta(3) = 0.83190737258... The number of cubefree integers not exceeding N is thus roughly N/zeta(3). When N is a power of 10, this sequence gives the difference between the actual number (A160112) and that linear estimate (rounded to the nearest integer). LINKS G. P. Michon, Reciprocal of Apery's constant. G. P. Michon, On the number of cubefree integers not exceeding N. Eric Weisstein's World of Mathematics, Cubefree. FORMULA a(n) = A160112(n)-round(10^n/zeta(3)) CROSSREFS A004709 (cubefree integers). A160112 & A160113 (counting cubefree integers). Sequence in context: A287316 A210472 A246106 * A213028 A109970 A116088 Adjacent sequences:  A160111 A160112 A160113 * A160115 A160116 A160117 KEYWORD easy,sign AUTHOR Gerard P. Michon, May 06 2009 STATUS approved

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