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A078401
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Triangle read by rows: T(n,k) = number of numbers <= k that are coprime to n, 1<=k<=n.
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0
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1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 3, 4, 4, 1, 1, 1, 1, 2, 2, 1, 2, 3, 4, 5, 6, 6, 1, 1, 2, 2, 3, 3, 4, 4, 1, 2, 2, 3, 4, 4, 5, 6, 6, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| T(n,1) = 1; T(n,n) = phi(n), where phi is Euler's totient function (A000010); for p prime: T(p,i) = i for 1<=i<p and T(p,p) = p-1.
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LINKS
| Eric Weisstein's World of Mathematics, Sieve of Eratosthenes.
Eric Weisstein's World of Mathematics, Legendre's Formula.
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FORMULA
| T(n,k) = Sum{mu(d)*floor(k/d): n mod d = 0}, where mu is the Moebius Function (A008683).
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CROSSREFS
| Sequence in context: A055230 A112050 A194884 * A086247 A116452 A103958
Adjacent sequences: A078398 A078399 A078400 * A078402 A078403 A078404
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KEYWORD
| nonn,tabl
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 25 2002
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EXTENSIONS
| Thanks to Duc Ngo Minh (ducnm0(AT)gmail.com) who noticed an error in the formula; corrected by Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 01 2009
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