Prime Curios!: 0.6079271018540266286...

0.6079271018540266286...
(another Prime Pages' Curiosity)

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0.607927 1018540266 2866327677 9258365833 4261526480 3347929307 3654191365 0387257734 1264714725 5643553731 0256817334 6656911431 7490084371 6059165104 7441602130 8980899558 3171258116 2369653909 6558718572 7476771991 8153049455 4110548956 5076615448 0139764521 9862471251 1154745307 6673818164 2288912218 1457470211 1582131423 1353827241 8843867...

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1/zeta(2) where zeta is the Riemann zeta function = 0.6079271018540266286... = the asymptotic density of squarefree numbers (also called quadratfrei), those whose prime decomposition contains no repeated factors. All primes are therefore trivially squarefree. The number 1 is by convention taken to be squarefree. The squarefree numbers are 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, .... Conversely, the squareful numbers (i.e., those that contain at least one square) are 4, 8, 9, 12, 16, 18, 20, 24, 25, .... [Post]

Submitted: 2005-07-04 18:46:02; Last Modified: 2009-03-01 13:16:55.