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.

Previous Showing 21-27 of 27 results.

A181449 Numbers k such that 7 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

6, 8, 13, 15, 29, 41, 55, 71, 97, 99, 127, 244, 251, 449, 4801, 8749
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 7.
Sequence is finite and complete, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(4) = 8749; primepi(7) = 4.

Crossrefs

Row 4 of A223701.
Cf. A076605, A175607, A181447, A181448, A181450-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..9000] | m eq 7 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 17 2011
  • Mathematica
    Select[Range[9000], FactorInteger[#^2-1][[-1, 1]]==7&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 5, n/=p^valuation(n, p)); n>1 && 7^valuation(n, 7)==n \\ Charles R Greathouse IV, Jul 01 2013

A181450 Numbers k such that 11 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

10, 21, 23, 34, 43, 65, 76, 89, 109, 111, 197, 199, 241, 351, 485, 769, 881, 1079, 6049, 19601
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 11.
Sequence is finite and complete, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(5) = 19601; primepi(11) = 5.

Crossrefs

Row 5 of A223701.
Cf. A076605, A175607, A181447-A181449, A181451-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..20000] | m eq 11 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 2011
  • Mathematica
    Select[Range[20000], FactorInteger[#^2-1][[-1, 1]]==11&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 7, n/=p^valuation(n, p)); n>1 && 11^valuation(n, 11)==n \\ Charles R Greathouse IV, Jul 01 2013

A181451 Numbers k such that 13 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

12, 14, 25, 27, 51, 53, 64, 79, 129, 131, 155, 181, 209, 274, 287, 337, 391, 649, 701, 703, 727, 846, 1249, 1351, 1457, 1574, 2001, 3431, 4159, 8191, 8449, 13311, 21295, 246401
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 13.
Sequence is finite and complete, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(6) = 246401; primepi(13) = 6.

Crossrefs

Row 6 of A223701.
Cf. A076605, A175607, A181447-A181450, A181452-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..250000] | m eq 13 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 2011
  • Mathematica
    Select[Range[250000], FactorInteger[#^2-1][[-1, 1]]==13&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 11, n/=p^valuation(n, p)); n>1 && 13^valuation(n, 13)==n \\ Charles R Greathouse IV, Jul 01 2013

A181454 Numbers k such that 23 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

22, 24, 45, 47, 91, 116, 137, 139, 183, 208, 229, 254, 298, 321, 323, 344, 415, 461, 505, 551, 599, 645, 781, 783, 919, 967, 1013, 1057, 1126, 1151, 1310, 1471, 1519, 1749, 1793, 2186, 2209, 2276, 2393, 2575, 2874, 2991, 3704, 3725, 4047, 4049, 4369
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 23.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(9) = 10285001; primepi(23) = 9.

Links

Crossrefs

Cf. A076605, A175607, A181447-A181453, A181455-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 23 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 2011
  • Magma
    p:=(97*89*83*79*73*71)^5 *(67*61*59*53*47*43*41)^6 *(37*31*29)^7 *(23*19*17)^8 *13^9 *11^10 *7^13 *5^15 *3^23 *2^36; [ n: n in [2..10300000] | p mod (n^2-1) eq 0 and (D[#D] eq 23 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 24 2011
  • Mathematica
    jj=2^36*3^23*5^15*7^13*11^10*13^9*17^8*19^8*23^8*29^7*31^7*37^7*41^6 *43^6*47^6*53^6*59^6*61^6*67^6*71^5*73^5*79^5*83^5*89^5*97^5; rr ={};n = 2; While[n < 14000000, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 23, AppendTo[rr, n]]]; n++ ]; rr
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==23&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 19, n/=p^valuation(n, p)); n>1 && 23^valuation(n, 23)==n \\ Charles R Greathouse IV, Jul 01 2013

A181456 Numbers k such that 31 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

30, 32, 61, 63, 92, 94, 125, 154, 185, 249, 309, 311, 342, 373, 404, 433, 495, 526, 528, 559, 681, 683, 714, 869, 898, 929, 991, 1055, 1084, 1177, 1241, 1301, 1427, 1520, 1611, 1673, 1735, 1799, 1861, 1921, 1954, 2047, 2107, 2419, 2696, 2729, 2851, 3037
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 31.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(11) = 3222617399; primepi(31) = 11.

Links

Crossrefs

Cf. A076605, A175607, A181447-A181455, A181457-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 31 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 2011
  • Magma
    p:=(97*89*83*79*73*71)^5 *(67*61*59*53*47*43*41)^6 *(37*31*29)^7 *(23*19*17)^8 *13^9 *11^10 *7^13 *5^15 *3^23 *2^36; [ n: n in [2..50000000] | p mod (n^2-1) eq 0 and (D[#D] eq 31 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 20 2011
  • Mathematica
    jj = 2^36*3^23*5^15*7^13*11^10*13^9*17^8*19^8*23^8*29^7*31^7*37^7*41^6 *43^6*47^6*53^6*59^6*61^6*67^6*71^5*73^5*79^5*83^5*89^5*97^5; rr = {}; n = 2; While[n < 3222617400, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 31, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[5000],Max[Transpose[FactorInteger[ #^2-1]][[1]]]==31&] (* Harvey P. Dale, Nov 03 2010 *)
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 29, n/=p^valuation(n, p)); n>1 && 31^valuation(n, 31)==n \\ Charles R Greathouse IV, Jul 01 2013

A199423 Greatest prime factor of n and 2*n+1.

Original entry on oeis.org

3, 5, 7, 3, 11, 13, 7, 17, 19, 7, 23, 5, 13, 29, 31, 11, 17, 37, 19, 41, 43, 11, 47, 7, 17, 53, 11, 19, 59, 61, 31, 13, 67, 23, 71, 73, 37, 19, 79, 5, 83, 17, 43, 89, 13, 31, 47, 97, 11, 101, 103, 13, 107, 109, 37, 113, 23, 29, 59, 11, 61, 31, 127, 43, 131, 19
Offset: 1

Views

Author

Franklin T. Adams-Watters, Nov 06 2011

Keywords

Links

Crossrefs

Cf. A006530, A014105, A074399, A093074, A076605.

Programs

  • Mathematica
    Table[Max[Flatten[FactorInteger[{n,2 n+1}],1][[All,1]]],{n,70}] (* Harvey P. Dale, Mar 25 2020 *)
  • PARI
    gpf(n)=local(ps);if(n<2,n,ps=factor(n)[,1]~;ps[#ps])
vector(80,n,gpf(n*(2*n+1)))

Formula

a(n) = A006530(A014105(n)).

A321069 Greatest prime factor of n^3+2.

Original entry on oeis.org

3, 5, 29, 11, 127, 109, 23, 257, 43, 167, 43, 173, 733, 1373, 307, 683, 983, 2917, 2287, 4001, 157, 71, 283, 223, 5209, 47, 127, 3659, 24391, 587, 9931, 113, 433, 6551, 809, 569, 307, 27437, 433, 10667, 439, 239, 1559, 223, 91127, 16223, 4153, 457, 39217, 62501
Offset: 1

Views

Author

Charles R Greathouse IV, Oct 27 2018

Keywords

Links

Crossrefs

Greatest prime factors of polynomials: A006530 (n), A076565 (2n+1), A076566 (3n+3), A076567 (4n+6), A164314 (n^2-2), A076605 (n^2-1), A014442 (n^2+1), A069902 (n^2+n), A074399 (n^2+n), A199423 (2n^2+n), A089619 (2n^2+2n+1), A037464 (4n^2-1), A253254 (9n^2-7n), A093074 (n^3-n), A081257 (n^3-1), A081256 (n^3+1), A321069(n^3+2), A281793 (n^3+n^2+n+1), A281793 (n^4-1), A096172 (n^4+1), A190136 (n^4 + 6n^3 + 11n^2 + 6n), A140538 (2n^4+1), A240548 (n^5+1), A281794 (n^5+n^3+n^2+1), A240549 (n^6+1), A240550 (n^7+1), A240551 (n^8+1), A240552 (n^9+1), A240553 (n^10+1).

Programs

  • Magma
    [Maximum(PrimeDivisors(n^3 + 2)): n in [1..60]]; // Vincenzo Librandi, Oct 27 2018
  • Mathematica
    Table[FactorInteger[n^3 + 2] [[-1, 1]], {n, 80}] (* Vincenzo Librandi, Oct 27 2018 *)
  • PARI
    a(n) = vecmax(factor(n^3+2)[,1]); \\ Michel Marcus, Oct 27 2018
Previous Showing 21-27 of 27 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.