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 11-20 of 27 results. Next

A181460 Numbers k such that 47 is the largest prime factor of k^2-1.

Original entry on oeis.org

46, 48, 93, 95, 142, 187, 189, 281, 375, 377, 424, 469, 610, 657, 659, 704, 751, 753, 892, 988, 1033, 1035, 1082, 1174, 1223, 1270, 1364, 1409, 1597, 1599, 1691, 1693, 1926, 1973, 1975, 2022, 2069, 2161, 2255, 2351, 2443, 2584, 2727, 2913, 2915, 3009
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 47.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(15) = 2218993446251; primepi(47) = 15.

Links

Crossrefs

Cf. A076605, A175607, A181447-A181459, A181461-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 47 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 2011
  • Mathematica
    Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==47&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 43, n/=p^valuation(n, p)); n>1 && 47^valuation(n, 47)==n \\ Charles R Greathouse IV, Jul 01 2013

A181461 Numbers k such that 53 is the largest prime factor of k^2-1.

Original entry on oeis.org

52, 54, 105, 107, 160, 211, 319, 370, 476, 529, 531, 584, 637, 741, 743, 847, 849, 900, 902, 953, 1059, 1220, 1273, 1324, 1377, 1379, 1483, 1538, 1644, 1695, 1801, 1803, 2015, 2174, 2278, 2386, 2437, 2543, 2651, 2755, 2861, 2969, 3073, 3181, 3497, 3499
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 53.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(16) = 2907159732049; primepi(53) = 16.

Links

Crossrefs

Cf. A076605, A175607, A181447-A181460, A181462-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 53 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 53 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 == 53, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==53&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 47, n/=p^valuation(n, p)); n>1 && 53^valuation(n, 53)==n \\ Charles R Greathouse IV, Jul 01 2013

A181462 Numbers k such that 59 is the largest prime factor of k^2-1.

Original entry on oeis.org

58, 117, 119, 176, 235, 237, 296, 353, 471, 530, 532, 589, 591, 650, 766, 827, 945, 1002, 1061, 1063, 1179, 1297, 1299, 1535, 1592, 1594, 1651, 1769, 1828, 1887, 1889, 2066, 2184, 2241, 2243, 2300, 2302, 2479, 2536, 2774, 2951, 3126, 3244, 3305, 3421
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 59.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(17) = 41257182408961; primepi(59) = 17.

Links

Crossrefs

Cf. A076605, A175607, A181447-A181461, A181463-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 59 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 59 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 == 59, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[10000],Max[Transpose[FactorInteger[#^2-1]][[1]]]==59&] (* Harvey P. Dale, Nov 13 2010 *)
  • PARI
    for(k=2,1e9,vecmax(factor(k^2-1)[,1])==59 & print1(k",")) \\ M. F. Hasler, Nov 13 2010

A181463 Numbers k such that 61 is the largest prime factor of k^2-1.

Original entry on oeis.org

60, 62, 121, 123, 184, 243, 245, 365, 367, 426, 428, 487, 489, 550, 609, 611, 794, 1036, 1099, 1160, 1219, 1221, 1343, 1463, 1585, 1646, 1709, 1768, 1770, 1951, 2014, 2073, 2256, 2319, 2439, 2441, 2500, 2561, 2624, 2807, 2927, 3173, 3537, 3539, 3659, 3781
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 61.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(18) = 63774701665793; primepi(61) = 18.

Links

Crossrefs

Cf. A076605, A175607, A181447-A181462, A181464-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 61 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 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 == 61, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==61&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 59, n/=p^valuation(n, p)); n>1 && 61^valuation(n, 61)==n \\ Charles R Greathouse IV, Jul 01 2013

A181464 Numbers k such that 67 is the largest prime factor of k^2-1.

Original entry on oeis.org

66, 68, 133, 135, 202, 267, 269, 334, 401, 604, 671, 736, 805, 937, 939, 1004, 1006, 1205, 1272, 1274, 1341, 1473, 1475, 1540, 1609, 1676, 1741, 2078, 2143, 2145, 2210, 2279, 2545, 2547, 2746, 2813, 2815, 2882, 2949, 3081, 3349, 3550, 3552, 3751, 3887
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 67.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(19) = 25640240468751; primepi(67) = 19.

Links

Crossrefs

Cf. A076605, A175607, A181447-A181463, A181465-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 67 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 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 == 67, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==67&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 61, n/=p^valuation(n, p)); n>1 && 67^valuation(n, 67)==n \\ Charles R Greathouse IV, Jul 01 2013

A181465 Numbers k such that 71 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

70, 141, 143, 214, 283, 285, 356, 425, 496, 569, 638, 709, 780, 782, 851, 853, 924, 993, 1135, 1208, 1277, 1279, 1561, 1563, 1703, 1847, 2058, 2129, 2131, 2344, 2413, 2626, 2699, 2839, 2841, 3054, 3265, 3267, 3336, 3338, 3409, 3478, 3480, 3551, 3620, 3691
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 71.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(20) = 238178082107393; primepi(71) = 20.

Links

Crossrefs

Row 20 of A223701.
Cf. A076605, A175607, A181447-A181464, A181466-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 71 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 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 == 71, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==71&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 67, n/=p^valuation(n, p)); n>1 && 71^valuation(n, 71)==n \\ Charles R Greathouse IV, Jul 01 2013

A181466 Numbers k such that 73 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

72, 74, 145, 147, 218, 220, 291, 293, 364, 439, 512, 729, 731, 804, 875, 1021, 1023, 1167, 1169, 1240, 1313, 1315, 1459, 1461, 1607, 1678, 1680, 1751, 1826, 1899, 2045, 2116, 2262, 2481, 2483, 2554, 2702, 2773, 2848, 3067, 3284, 3359, 3576, 3649, 3722
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 73.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(21) = 4573663454608289; primepi(73) = 21.

Links

Crossrefs

Row 21 of A223701
Cf. A076605, A175607, A181447-A181465, A181467-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 73 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 21 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 73 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 21 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 == 73, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==73&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 71, n/=p^valuation(n, p)); n>1 && 73^valuation(n, 73)==n \\ Charles R Greathouse IV, Jul 01 2013

A181467 Numbers k such that 79 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

78, 80, 157, 159, 236, 317, 473, 475, 552, 554, 631, 712, 791, 868, 870, 947, 949, 1026, 1028, 1105, 1184, 1421, 1737, 1739, 1816, 1897, 2053, 2134, 2211, 2213, 2369, 2450, 2529, 2685, 2687, 2843, 2924, 3001, 3161, 3477, 3554, 3870, 3949, 3951, 4186, 4188
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 79.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(22) = 19182937474703818751; primepi(79) = 22.

Links

Crossrefs

Row 22 of A223701.
Cf. A076605, A175607, A181447-A181466, A181468-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 79 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 21 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 79 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 21 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 == 79, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==79&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 73, n/=p^valuation(n, p)); n>1 && 79^valuation(n, 79)==n \\ Charles R Greathouse IV, Jul 01 2013

A181468 Numbers k such that 83 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

82, 84, 165, 167, 248, 331, 414, 497, 499, 582, 665, 829, 831, 914, 995, 1080, 1161, 1246, 1327, 1329, 1495, 1576, 1825, 1910, 2076, 2157, 2159, 2323, 2406, 2408, 2738, 2821, 2906, 2989, 3070, 3238, 3319, 3485, 3568, 3651, 3653, 3817, 4149, 4234, 4481
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 83.
Sequence is finite, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(23) = 34903240221563713 = a(2082); pi(83) = 23.

Links

Crossrefs

Row 23 of A223701.
Cf. A000720, A076605, A175607, A181447-A181467, A181469-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..300000] | m eq 83 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 21 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 83 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 21 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 == 83, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==83&]
  • PARI
    is(n)=n=n^2-1; forprime(p=2, 79, n/=p^valuation(n, p)); n>1 && 83^valuation(n, 83)==n \\ Charles R Greathouse IV, Jul 01 2013

A181448 Numbers k such that 5 is the largest prime factor of k^2 - 1.

Original entry on oeis.org

4, 9, 11, 19, 26, 31, 49, 161
Offset: 1

Views

Author

Artur Jasinski, Oct 21 2010

Keywords

Comments

Numbers k such that A076605(k) = 3.
Sequence is finite and complete, for proof see A175607.
Search for terms can be restricted to the range from 2 to A175607(3) = 161; primepi(5) = 3.

Crossrefs

Row 3 of A223701.
Cf. A076605, A175607, A181447, A181449-A181470, A181568.

Programs

  • Magma
    [ n: n in [2..200] | m eq 5 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 17 2011
  • Mathematica
    Select[Range[200], FactorInteger[#^2-1][[-1, 1]]==5&]
  • PARI
    is(n)=n=n^2-1; n>>=valuation(n,2); n/=3^valuation(n,3); n>1 && 5^valuation(n, 5)==n \\ Charles R Greathouse IV, Jul 01 2013
Previous Showing 11-20 of 27 results. Next

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

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