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 1-5 of 5 results.

A075592 Numbers n such that number of distinct prime divisors of n is a divisor of n.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 71, 72, 73, 74, 76, 78, 79, 80, 81, 82, 83, 84, 86, 88, 89, 90
Offset: 1

Views

Author

Amarnath Murthy, Sep 26 2002

Keywords

Comments

Numbers n such that omega(n) divides n.
The asymptotic density of this sequence is 0 (Cooper and Kennedy, 1989). - Amiram Eldar, Jul 10 2020

Links

Crossrefs

Different from A070776: 78 belongs to this sequence but not to A070776.
Cf. A185307 (complement), A001221, A001222, A074946 (BigOmega(n) divides n).

Programs

  • Mathematica
    Select[Range[2,100],Divisible[#,Length[Select[Divisors[#], PrimeQ]]]&]  (* Harvey P. Dale, Mar 17 2011 *)
  • PARI
    isok(n) = iferr(!(n % omega(n)), E, 0); \\ Michel Marcus, Oct 06 2017
  • R
    library(gmp); omega<-function(x) length(unique(as.numeric(factorize(x))))
which(c(F,vapply(2:100,function(n) isint(n/omega(n)),T))) # Christian N. K. Anderson, Apr 25 2013

Extensions

More terms from David Wasserman, Jan 20 2005
"Distinct" added to name by Christian N. K. Anderson, Apr 23 2013

A231876 Numbers n such that omega(n)^2 (cf. A001221) divides n.

Original entry on oeis.org

2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 19, 20, 23, 24, 25, 27, 28, 29, 31, 32, 36, 37, 40, 41, 43, 44, 47, 48, 49, 52, 53, 56, 59, 61, 64, 67, 68, 71, 72, 73, 76, 79, 80, 81, 83, 88, 89, 90, 92, 96, 97, 100, 101, 103, 104, 107, 108, 109, 112, 113, 116, 121, 124, 125, 126, 127, 128, 131, 136, 137, 139, 144, 148, 149
Offset: 1

Views

Author

N. J. A. Sloane, Nov 17 2013

Keywords

Comments

Includes all prime powers (A246655), as well as 4*A246655. - Robert Israel, Apr 25 2017

Links

Crossrefs

Cf. A001221, A075592, A185307, A001222, A074946, A134334, A231877 (complement).
Cf. A246655.

Programs

  • Maple
    select(n -> n mod nops(numtheory:-factorset(n))^2 = 0, [$2..1000]); # Robert Israel, Apr 25 2017
  • Mathematica
    Select[Range[2, 500], Mod[#, PrimeNu[#]^2] == 0  &] (* G. C. Greubel, Apr 24 2017 *)
  • PARI
    isok(n) = !(n % omega(n)^2); \\ Michel Marcus, Apr 25 2017

A231877 Numbers n such that omega(n)^2 (cf. A001221) does not divide n.

Original entry on oeis.org

1, 6, 10, 14, 15, 18, 21, 22, 26, 30, 33, 34, 35, 38, 39, 42, 45, 46, 50, 51, 54, 55, 57, 58, 60, 62, 63, 65, 66, 69, 70, 74, 75, 77, 78, 82, 84, 85, 86, 87, 91, 93, 94, 95, 98, 99, 102, 105, 106, 110, 111, 114, 115, 117, 118, 119, 120, 122, 123, 129, 130, 132, 133, 134, 135, 138, 140, 141, 142, 143, 145, 146, 147, 150
Offset: 1

Views

Author

N. J. A. Sloane, Nov 17 2013

Keywords

Links

Crossrefs

Cf. A001221, A075592, A185307, A001222, A074946, A134334, A231876 (complement).

Programs

  • Mathematica
    Join[{1}, Select[Range[2, 500], Mod[#, PrimeNu[#]^2] != 0  &]] (* G. C. Greubel, Apr 24 2017 *)

A231878 Numbers k such that bigomega(k)^2 (cf. A001222) divides k.

Original entry on oeis.org

2, 3, 4, 5, 7, 11, 13, 16, 17, 18, 19, 23, 27, 29, 31, 37, 41, 43, 45, 47, 53, 59, 61, 63, 67, 71, 73, 79, 83, 89, 97, 99, 101, 103, 107, 109, 113, 117, 127, 131, 137, 139, 144, 149, 151, 153, 157, 163, 167, 171, 173, 179, 181, 191, 193, 197, 199, 200, 207, 211, 216, 223, 227, 229, 233, 239, 241, 251, 256, 257, 261, 263
Offset: 1

Views

Author

N. J. A. Sloane, Nov 17 2013

Keywords

Comments

Contains all primes. - Ivan Neretin, Apr 05 2016

Links

Crossrefs

Cf. A001221, A075592, A185307, A001222, A074946, A134334, A231879 (complement).

Programs

  • Mathematica
    Select[Range[2, 265], Divisible[#, PrimeOmega[#]^2] &] (* Ivan Neretin, Apr 05 2016 *)
  • PARI
    isok(n) = !(n % bigomega(n)^2); \\ Michel Marcus, Apr 05 2016

A231879 Numbers n such that bigomega(n)^2 (cf. A001222) does not divide n.

Original entry on oeis.org

1, 6, 8, 9, 10, 12, 14, 15, 20, 21, 22, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115
Offset: 1

Views

Author

N. J. A. Sloane, Nov 17 2013

Keywords

Comments

Contains all semiprimes (A001358) except 4. - Ivan Neretin, Apr 05 2016

Links

Crossrefs

Cf. A001221, A075592, A185307, A001222, A074946, A134334, A231878 (complement).

Programs

  • Mathematica
    Join[{1}, Select[Range[2, 115], ! Divisible[#, PrimeOmega[#]^2] &]] (* Ivan Neretin, Apr 05 2016 *)
  • PARI
    lista(nn) = {print1(1, ", "); for(n=2, nn, if(n % bigomega(n)^2 != 0, print1(n, ", ")));} \\ Altug Alkan, Apr 05 2016
Showing 1-5 of 5 results.

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

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