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 1-3 of 3 results.

A075819 Even squarefree numbers with exactly 3 prime factors.

Original entry on oeis.org

30, 42, 66, 70, 78, 102, 110, 114, 130, 138, 154, 170, 174, 182, 186, 190, 222, 230, 238, 246, 258, 266, 282, 286, 290, 310, 318, 322, 354, 366, 370, 374, 402, 406, 410, 418, 426, 430, 434, 438, 442, 470, 474, 494, 498, 506, 518, 530, 534, 574, 582, 590
Offset: 1

Views

Author

Jani Melik, Oct 13 2002

Keywords

Comments

This sequence first differs from A053858 at 2310=2*3*5*7*11, which is in A053858 but not in this sequence.

Examples

			30=2*3*5 and 42=2*3*7 are even, squarefree and have 3 prime factors.

Links

Crossrefs

Cf. A046388, A053858.

Programs

  • Maple
    ts_3_sod := proc(n); if (numtheory[bigomega](n)=3 and numtheory[mobius](n)=-1 and type(n,even)='true') then RETURN(n); fi end: a3sod := [seq(ts_3_sod(i), i=1..2500)]: a3sod;
  • Mathematica
    Select[2*Range[300],SquareFreeQ[#]&&PrimeNu[#]==3&] (* Harvey P. Dale, Feb 16 2018 *)
  • PARI
    list(lim)=my(v=List()); forprime(p=5, lim\6, forprime(q=3, min(lim\(2*p),p-2), listput(v, 2*p*q))); Set(v) \\ Charles R Greathouse IV, Aug 29 2017

Formula

a(n) = 2 * A046388(n). - Amiram Eldar, Mar 03 2021

Extensions

Edited by Dean Hickerson, Oct 21 2002

A075818 Even numbers with exactly 3 prime factors (counted with multiplicity).

Original entry on oeis.org

8, 12, 18, 20, 28, 30, 42, 44, 50, 52, 66, 68, 70, 76, 78, 92, 98, 102, 110, 114, 116, 124, 130, 138, 148, 154, 164, 170, 172, 174, 182, 186, 188, 190, 212, 222, 230, 236, 238, 242, 244, 246, 258, 266, 268, 282, 284, 286, 290, 292, 310, 316, 318, 322, 332, 338
Offset: 1

Views

Author

Jani Melik, Oct 13 2002

Keywords

Comments

Twice the semiprime numbers. - Juri-Stepan Gerasimov, Jun 01 2010

Examples

			28=2^2*7, 30=2*3*5 and 42=2*3*7 are even and are products of exactly 3 primes.

Links

Crossrefs

Cf. A046470, A053858.

Programs

  • Magma
    [2*n: n in [2..200] | &+[d[2]: d in Factorization(n)] eq 2]; // Vincenzo Librandi Nov 10 2018
  • Maple
    ts_bo3_sod := proc(n); if (numtheory[bigomega](n)=3 and type(n,even)='true') then RETURN(n); fi end: abo3sod := [seq(ts_bo3_sod(i), i=1..2300)]: abo3sod;
  • Mathematica
    Select[Range[100], Plus@@Last/@FactorInteger[#]==2&] 2 (* Vincenzo Librandi, Nov 10 2018 *)
Select[Range[2,400,2],PrimeOmega[#]==3&] (* Harvey P. Dale, Oct 15 2021 *)
  • PARI
    list(lim)=my(v=List()); forprime(p=2, lim\4, forprime(q=2, min(lim\p\2,p), listput(v, 2*p*q))); Set(v) \\ Charles R Greathouse IV, Aug 29 2017

Formula

a(n)=2*A001358(n). - Juri-Stepan Gerasimov, Jun 01 2010

Extensions

Edited by Dean Hickerson, Oct 21 2002

A075809 Palindromic even numbers with an odd number of distinct prime factors.

Original entry on oeis.org

2, 66, 222, 282, 434, 474, 494, 606, 646, 2222, 2882, 4334, 4994, 6006, 6226, 6446, 6886, 8338, 8558, 8778, 8998, 20002, 20202, 20702, 20802, 20902, 22222, 22922, 24042, 24342, 24542, 24742, 24942, 26062, 26162, 26462, 28082, 28182, 28282
Offset: 1

Views

Author

Jani Melik, Oct 13 2002

Keywords

Examples

			66=2*3*11, 222=2*3*37 and 282=2*3*47 are palindromic, even and products of an odd number of distinct primes.

Links

Crossrefs

Cf. A053858.

Programs

  • Maple
    test := proc(n) local d; d := convert(n,base,10); return ListTools[Reverse](d)=d and numtheory[mobius](n)=-1; end; a := []; for n from 2 to 30000 by 2 do if test(n) then a := [op(a),n]; end; od; a;

Extensions

Edited by Dean Hickerson, Oct 21 2002
Showing 1-3 of 3 results.

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