cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A348709 Number of squarefree integers with an even number of prime factors <= 10^n.

Original entry on oeis.org

1, 3, 31, 305, 3030, 30373, 304069, 3040164, 30397311, 303963451, 3039618610, 30396311212, 303963582320, 3039635808938, 30396354655186, 303963549318865, 3039635507672484, 30396355081786770, 303963550903632005, 3039635509720135531, 30396355092931863204, 303963550925315375170
Offset: 0

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Author

Giorgos Kalogeropoulos, Oct 30 2021

Keywords

Comments

a(n) is the number of integers k <= 10^n with mu(k)=1 where mu(k) is the Möbius function.

Examples

			a(1) = 3 because there are 3 squarefree integers with an even number of prime factors <= 10: 1, 6, 10.

Crossrefs

Cf. A071172, A084237, A008683, A030229, A104141, A348708.

Programs

  • Mathematica
    Table[Length@Select[Range[10^n],MoebiusMu@#==1&],{n,0,6}]

Formula

a(n) = (A071172(n) + A084237(n)) / 2.
Lim_{n->oo} a(n)/10^n = 3/Pi^2 (A104141).
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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