A247892 -id:A247892 - cp's OEIS frontend

A077581 Triangle in which row n contains the n smallest numbers starting from 1 and coprime to n.

1, 1, 3, 1, 2, 4, 1, 3, 5, 7, 1, 2, 3, 4, 6, 1, 5, 7, 11, 13, 17, 1, 2, 3, 4, 5, 6, 8, 1, 3, 5, 7, 9, 11, 13, 15, 1, 2, 4, 5, 7, 8, 10, 11, 13, 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Offset: 1

Amarnath Murthy, Nov 14 2002

A247815 and A247892 give number of primes and nonprimes per row. - Reinhard Zumkeller, Sep 26 2014

			1;
1,  3;
1,  2,  4;
1,  3,  5,  7;
1,  2,  3,  4,  6;
1,  5,  7, 11, 13, 17;
1,  2,  3,  4,  5,  6,  8;
1,  3,  5,  7,  9, ...

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Cf. A069213, A077582.
Cf. A247798 (central terms), A247815, A247892.
Cf. A077664.

a077581 n k = a077581_tabl !! (n-1) !! (k-1)
a077581_row n = a077581_tabl !! (n-1)
a077581_tabl = map (\x -> take x [z | z <- [1..], gcd x z == 1]) [1..]
-- Reinhard Zumkeller, Sep 26 2014

row[n_] := Take[Select[Range[n^2], GCD[ #, n]==1&], n]; Join@@row/@Range[13]

More terms from Sascha Kurz, Jan 11 2003

A247815 Number of primes in n-th row of triangle A077581.

Original entry on oeis.org

0, 1, 1, 3, 2, 5, 3, 5, 5, 7, 4, 9, 5, 9, 7, 10, 6, 14, 7, 13, 10, 13, 8, 18, 10, 14, 11, 16, 9, 26, 10, 17, 14, 18, 13, 26, 11, 20, 16, 23, 12, 31, 13, 22, 21, 22, 14, 32, 15, 28, 20, 27, 15, 35, 19, 29, 22, 28, 16, 45, 17, 29, 27, 30, 21, 44, 18, 32, 26

Offset: 1

Reinhard Zumkeller, Sep 26 2014

nonn

a(n) = n - A247892(n).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000720, A001221, A010051, A069213, A077581, A247892.

a247815 = sum . map a010051' . a077581_row

a(n) = A000720(A069213(n)) - A001221(n).

cp's OEIS Frontend

A077581 Triangle in which row n contains the n smallest numbers starting from 1 and coprime to n.

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