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.

Showing 1-10 of 16 results. Next

A077580 Duplicate of A069213.

Original entry on oeis.org

1, 3, 4, 7, 6, 17, 8, 15, 13, 23, 12, 35, 14, 31, 28, 31, 18, 53, 20, 49, 37, 47, 24, 71, 31
Offset: 1

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Author

Keywords

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

Original entry on oeis.org

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

Views

Author

Amarnath Murthy, Nov 14 2002

Keywords

Comments

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

Examples

			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, ...

Links

Crossrefs

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

Programs

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

Extensions

More terms from Sascha Kurz, Jan 11 2003

A077582 Sum of terms of n-th row of A077581.

Original entry on oeis.org

1, 4, 7, 16, 16, 54, 29, 64, 61, 124, 67, 216, 92, 228, 211, 256, 154, 486, 191, 500, 385, 532, 277, 864, 391, 732, 547, 914, 436, 1688, 497, 1024, 895, 1228, 890, 1944, 704, 1524, 1232, 2000, 862, 3090, 947, 2128, 1897, 2212, 1129, 3456, 1401, 3124, 2068
Offset: 1

Views

Author

Amarnath Murthy, Nov 14 2002

Keywords

Comments

a(p) = p(p-1)/2 + p+1 = (p^2 + p + 2)/2, if p is a prime. a(2^n) = 2^(2n).

Links

Crossrefs

Cf. A069213, A077581.

Programs

Extensions

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

Views

Author

Reinhard Zumkeller, Sep 26 2014

Keywords

Comments

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

Links

Crossrefs

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

Programs

  • Haskell
    a247815 = sum . map a010051' . a077581_row

Formula

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

A077662 a(n) = n-th positive integer not relatively prime to n, with a(1)=1.

Original entry on oeis.org

1, 4, 9, 8, 25, 9, 49, 16, 27, 16, 121, 18, 169, 24, 33, 32, 289, 27, 361, 34, 49, 40, 529, 36, 125, 48, 81, 49, 841, 40, 961, 64, 84, 64, 112, 54, 1369, 72, 102, 66, 1681, 58, 1849, 80, 96, 88, 2209, 72, 343, 84, 136, 96, 2809, 81, 200, 98, 153, 112, 3481, 82
Offset: 1

Views

Author

Amarnath Murthy, Nov 14 2002

Keywords

Comments

Final term of n-th row of A077661.

Links

Crossrefs

Cf. A077661, A077663, A069213.
A077149(n) - n - 1.

Programs

  • Mathematica
    Join[{1},Table[Select[Range[5000],!CoprimeQ[#,n]&][[n]],{n,2,60}]] (* Harvey P. Dale, May 26 2023 *)
  • PARI
    a(n) = local(i, k); if(n<=1,n,k=n-eulerphi(n);i=n\k;k*=i;i*=n; while(k

Extensions

More terms from Sascha Kurz, Jan 27 2003

A077665 Final term of n-th row of A077664.

Original entry on oeis.org

2, 5, 7, 11, 11, 23, 15, 23, 22, 33, 23, 47, 27, 45, 43, 47, 35, 71, 39, 69, 58, 69, 47, 95, 56, 81, 67, 93, 59, 139, 63, 95, 86, 105, 86, 143, 75, 117, 101, 139, 83, 187, 87, 139, 128, 141, 95, 191, 106, 173, 131, 163, 107, 215, 129, 185, 146, 177, 119, 283, 123, 189
Offset: 1

Views

Author

Amarnath Murthy, Nov 14 2002

Keywords

Comments

a(p) = 2p+1, p is a prime. a(2^n) = 3*2^n -1.
a(n) also equals the (n+phi(n))th integer from among those positive integers coprime to n, where phi(n) = A000010(n). a(n) also equals n + (the n-th integer from among those positive integers coprime to n) = n + A069213(n). - Leroy Quet, Apr 12 2007

Links

Crossrefs

Cf. A077664, A077666.

Programs

Extensions

More terms from Sascha Kurz, Jan 03 2003

A247798 n-th positive integer relatively prime to 2*n - 1.

Original entry on oeis.org

1, 2, 3, 4, 7, 6, 7, 14, 9, 10, 19, 12, 16, 20, 15, 16, 28, 26, 19, 32, 21, 22, 43, 24, 29, 41, 27, 38, 46, 30, 31, 55, 44, 34, 55, 36, 37, 71, 50, 40, 61, 42, 57, 68, 45, 58, 73, 63, 49, 82, 51, 52, 116, 54, 55, 86, 57, 76, 95, 74, 67, 95, 78, 64, 100, 66
Offset: 1

Views

Author

Reinhard Zumkeller, Sep 26 2014

Keywords

Comments

Central terms of triangle A077581.

Links

Crossrefs

Cf. A077581, A069213.

Programs

  • Haskell
    a247798 n = a077581 (2 * n - 1) n

A126356 a(n) is the n-th integer from among the positive integers which are coprime to (n+1).

Original entry on oeis.org

1, 2, 5, 4, 13, 6, 13, 11, 21, 10, 31, 12, 29, 26, 29, 16, 49, 18, 47, 34, 45, 22, 67, 29, 53, 38, 61, 28, 107, 30, 61, 52, 69, 48, 103, 36, 77, 61, 97, 40, 143, 42, 93, 82, 93, 46, 139, 55, 121, 79, 109, 52, 157, 73, 127, 88, 117, 58, 221, 60, 125, 107, 125, 86, 215, 66, 141
Offset: 1

Views

Author

Leroy Quet, Dec 26 2006

Keywords

Examples

			The positive integers which are coprime to 6 are 1,5,7,11,13,17,19,23,... The 5th of these is 13, which is a(5).

Crossrefs

Cf. A069213, A126357.

Programs

  • Mathematica
    f[n_] := Block[{k = 0, c = n},While[c > 0,k++;While[GCD[k, n + 1] > 1, k++ ];c--;];k];Table[f[n], {n, 67}] (* Ray Chandler, Dec 29 2006 *)

Extensions

Extended by Ray Chandler, Dec 29 2006

A126357 a(n) is the (n+1)st integer from among the positive integers which are coprime to n.

Original entry on oeis.org

2, 5, 5, 9, 7, 19, 9, 17, 14, 27, 13, 37, 15, 33, 29, 33, 19, 55, 21, 51, 38, 49, 25, 73, 32, 57, 41, 67, 31, 113, 33, 65, 56, 73, 52, 109, 39, 81, 64, 101, 43, 149, 45, 97, 86, 97, 49, 145, 58, 127, 82, 113, 55, 163, 76, 131, 91, 121, 61, 227, 63, 129, 110, 129, 88, 221, 69
Offset: 1

Views

Author

Leroy Quet, Dec 26 2006

Keywords

Examples

			The positive integers which are coprime to 6 are 1,5,7,11,13,17,19,23,... The 7th of these is 19, which is a(6).

Crossrefs

Cf. A069213, A126356.

Programs

  • Mathematica
    f[n_] := Block[{k = 0, c = n + 1},While[c > 0,k++;While[GCD[k, n] > 1, k++ ];c--;];k];Table[f[n], {n, 67}] (* Ray Chandler, Dec 29 2006 *)

Extensions

Extended by Ray Chandler, Dec 29 2006

A105054 a(n) is the n-th positive integer among those which do not occur earlier in the sequence and which are coprime to n.

Original entry on oeis.org

1, 5, 7, 13, 8, 29, 11, 25, 22, 37, 17, 61, 20, 51, 44, 49, 27, 85, 32, 77, 59, 75, 38, 113, 47, 93, 68, 101, 45, 163, 52, 105, 83, 115, 76, 167, 58, 131, 103, 149, 66, 221, 70, 153, 133, 155, 74, 223, 90, 187, 127, 183, 87, 251, 109, 207, 142, 193, 95, 329, 98, 205, 173
Offset: 1

Views

Author

Leroy Quet, Apr 04 2005

Keywords

Examples

			a(4) is the 4th positive integer coprime to 4 and not among the first 3 terms of the sequence (i.e. the 4th term among 3, 9, 11, 13, 15,...).

Crossrefs

Cf. A069213.

Extensions

More terms from John W. Layman, Apr 08 2005
Showing 1-10 of 16 results. Next

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