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 1-4 of 4 results.

A124941 Numbers k such that k and k+4 are 4-almost primes.

Original entry on oeis.org

36, 56, 84, 100, 132, 136, 152, 228, 340, 344, 372, 376, 472, 484, 488, 532, 546, 564, 568, 580, 621, 632, 686, 708, 770, 804, 808, 820, 846, 852, 856, 868, 872, 950, 1012, 1192, 1204, 1206, 1208, 1274, 1304, 1326, 1336, 1444, 1524, 1550, 1572, 1576, 1690
Offset: 1

Views

Author

Zak Seidov, Nov 13 2006

Keywords

Examples

			36=2^2*3^2, 40=2^3*5; 56=2^3*7, 60=2^2*3*5.

Links

Crossrefs

Cf. A014613, A124940, A124942, A157483, A180117.

Programs

  • Mathematica
    Select[Range[1690], PrimeOmega[#]==PrimeOmega[#+4]==4 &] (* James C. McMahon, Dec 07 2024 *)
  • PARI
    isok(n) = (bigomega(n) == 4) && (bigomega(n+4) == 4); \\ Michel Marcus, Oct 11 2013

A124942 Numbers k such that k and k+5 are 5-almost primes.

Original entry on oeis.org

675, 1323, 1372, 1480, 1750, 1875, 2295, 2920, 3100, 3856, 4095, 4120, 4180, 4275, 4375, 5175, 5427, 5643, 5775, 5980, 6370, 6375, 6520, 6723, 6820, 7150, 7155, 7203, 7240, 7245, 7960, 8325, 8883, 8920, 9075, 9207, 9555, 9620, 9625, 9747, 9855, 9940
Offset: 1

Views

Author

Zak Seidov, Nov 13 2006

Keywords

Examples

			675=3^3*5^2, 680=2^3*5*17; 1323=3^3*7^2, 1328=2^4*83.

Links

Crossrefs

Cf. A124940, A124941.

Programs

  • Mathematica
    Select[Range[10000],PrimeOmega[#]==PrimeOmega[#+5]==5&] (* James C. McMahon, Dec 13 2024 *)
Select[Partition[Range[10000],6,1],PrimeOmega[#[[1]]]==PrimeOmega[#[[6]]]==5&][[;;,1]] (* Harvey P. Dale, Aug 27 2025 *)
  • PARI
    isok(n) = (bigomega(n) == 5) && (bigomega(n+5) == 5); \\ Michel Marcus, Oct 11 2013

A124945 Numbers k such that k and k+10 are 10-almost primes.

Original entry on oeis.org

506240, 789750, 1325312, 1567350, 1761750, 1944800, 2450240, 2579840, 3004928, 3013686, 3093750, 3153654, 3713526, 3844736, 3906240, 4024566, 4394240, 5244416, 5402240, 5431040, 6208640, 6310710, 6932790, 7053750, 7352694, 7585974, 8005878, 8043776, 8099190
Offset: 1

Views

Author

Zak Seidov, Nov 13 2006

Keywords

Comments

First term 506240 = A098515(10).

Examples

			506240=2^7*5*7*113, 506250=2*3^4*5^5;
789750=2*3^5*5^3*13, 789760=2^8*5*617;
1325312=2^8*31*167, 1325322=2*3^8*101;
1567350=2*3^6*5^2*43, 1567360=2^7*5*31*79.

Links

Crossrefs

Cf. A098515, A124940, A124941, A124942.

Programs

  • Mathematica
    Select[Range[10^7],PrimeOmega[#]==PrimeOmega[#+10]==10&] (* James C. McMahon, Dec 14 2024 *)
  • PARI
    isok(n) = (bigomega(n) == 10) && (bigomega(n+10) == 10); \\ Michel Marcus, Oct 11 2013
  • PARI
    P=prod(i=1,25,prime(i))^10; v=List(); for(n=1,1e6, g1=gcd(n,P); o1=bigomega(g1); if(o1<5,next); g2=gcd(n+10,P); o2=bigomega(g2); if(o2>=5 && o1+bigomega(n/g1)==10 && o2+bigomega((n+10)/g2)==10, listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Oct 11 2013

Extensions

More terms from Michel Marcus, Oct 11 2013

A124946 n and n+9 are 9-almost primes.

Original entry on oeis.org

268992, 338976, 516375, 675783, 922176, 984375, 1060695, 1107351, 1164375, 1216215, 1233216, 1361367, 1388736, 1458720, 1668672, 1843632, 1877175, 2018592, 2075463, 2317491, 2333520, 2395575, 2440935, 2457936, 2495367, 2499255, 2546775, 2559375, 2811744
Offset: 1

Views

Author

Zak Seidov, Nov 13 2006

Keywords

Comments

First term 268992 = A098515(9).
The first term not divisible by 9 is a(163) = 9384375. The first term not divisible by 3 is a(193) = 10504375. - Charles R Greathouse IV, Oct 11 2013

Examples

			268992=2^6*3^2*467, 268992+9=269001=3^8*41;
338976=2^5*3^2*11*107, 338976+9=338985=3^7*5*31.

Links

Crossrefs

Cf. A098515, A124940, A124941, A124942, A124945.

Programs

  • PARI
    isok(n) = (bigomega(n) == 9) && (bigomega(n+9) == 9); \\ Michel Marcus, Oct 11 2013

Extensions

More terms from Michel Marcus, Oct 11 2013
Showing 1-4 of 4 results.

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