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A078401 Triangle read by rows: T(n,k) = number of numbers <= k that are coprime to n, 1<=k<=n. 2
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; text; internal format)
OFFSET
1,5
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.
LINKS
Eric Weisstein's World of Mathematics, Sieve of Eratosthenes.
Eric Weisstein's World of Mathematics, Legendre's Formula.
FORMULA
T(n,k) = Sum{mu(d)*floor(k/d): n mod d = 0}, where mu is the Moebius Function (A008683).
EXAMPLE
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,
MAPLE
A078401 := proc(n, k)
a := 0 ;
for j from 1 to k do
if igcd(j, n) = 1 then
a := a+1 ;
end if;
end do:
a ;
end proc: # R. J. Mathar, Jul 21 2016
MATHEMATICA
T[n_, k_] := Count[Range[k], d_ /; CoprimeQ[n, d]];
Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 13 2018 *)
CROSSREFS
Sequence in context: A298231 A320473 A194884 * A271381 A086247 A116452
KEYWORD
nonn,tabl,easy
AUTHOR
Reinhard Zumkeller, Dec 25 2002
EXTENSIONS
Thanks to Duc Ngo Minh (ducnm0(AT)gmail.com) who noticed an error in the formula; corrected by Reinhard Zumkeller, Mar 01 2009
STATUS
approved

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Last modified April 23 09:48 EDT 2024. Contains 371905 sequences. (Running on oeis4.)