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.

A066499 Numbers k such that phi(k) == 2 (mod 4).

Original entry on oeis.org

3, 4, 6, 7, 9, 11, 14, 18, 19, 22, 23, 27, 31, 38, 43, 46, 47, 49, 54, 59, 62, 67, 71, 79, 81, 83, 86, 94, 98, 103, 107, 118, 121, 127, 131, 134, 139, 142, 151, 158, 162, 163, 166, 167, 179, 191, 199, 206, 211, 214, 223, 227, 239, 242, 243, 251, 254, 262, 263, 271
Offset: 1

Views

Author

Benoit Cloitre, Jan 04 2002

Keywords

Comments

Related to the equation x^4 = 1 (mod y): sequence gives values of n such x^4 = 1 (mod n) has no solution 1 < x < n-1.
k is of the form p^m or 2*p^m where p is A002145 (with the exception of a(2)=4).
All prime numbers here belong also to A002145, prime numbers of the form 4n+3. - Enrique Pérez Herrero, Sep 07 2011

References

  • W. J. LeVeque, Fundamentals of Number Theory, pp. 57 Problem 15, Dover NY 1996.

Links

Crossrefs

Cf. A066498, A066500, A066501, A066502, A000010.
Essentially the same as A097987.
Cf. A002145.

Programs

  • Mathematica
    Select[Range[300],Mod[EulerPhi[#],4]==2&] (* Harvey P. Dale, Feb 18 2018 *)
  • PARI
    isok(k) = { eulerphi(k)%4 == 2 } \\ Harry J. Smith, Feb 18 2010

Extensions

Simpler definition from Lekraj Beedassy, Jul 21 2003
Corrected and extended by Ray Chandler, Nov 06 2003

A172019 Numbers k such that 4 divides phi(k) (i.e., A000010(k)).

Original entry on oeis.org

5, 8, 10, 12, 13, 15, 16, 17, 20, 21, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 48, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 82, 84, 85, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 99, 100, 101
Offset: 1

Views

Author

Giovanni Teofilatto, Jan 22 2010

Keywords

Comments

Complement of A097987.
The asymptotic density of this sequence is 1 (Dressler, 1975). - Amiram Eldar, Feb 12 2021

Links

Crossrefs

Cf. A000010, A097987, A066499, A066498, A066500, A066502.

Programs

  • Mathematica
    Select[Range[200], Mod[EulerPhi[#], 4] == 0 &] (* Geoffrey Critzer, Nov 30 2014 *)
  • PARI
    is(n)=my(o=valuation(n, 2), p); (o>1 || !isprimepower(n>>o, &p) || p%4<2) && n>4 \\ Charles R Greathouse IV, Mar 05 2013

A292762 Numbers of the form p^k or 2*p^k, where p is a prime == 3 mod 4 and k is odd.

Original entry on oeis.org

3, 6, 7, 11, 14, 19, 22, 23, 27, 31, 38, 43, 46, 47, 54, 59, 62, 67, 71, 79, 83, 86, 94, 103, 107, 118, 127, 131, 134, 139, 142, 151, 158, 163, 166, 167, 179, 191, 199, 206, 211, 214, 223, 227, 239, 243, 251, 254, 262, 263, 271, 278, 283, 302, 307, 311, 326, 331, 334, 343, 347, 358, 359, 367, 379, 382
Offset: 1

Views

Author

N. J. A. Sloane, Sep 26 2017

Keywords

Comments

Numbers m such that sigma(m) == 0 mod 4 and phi(m) == 2 mod 4.

Links

Crossrefs

Intersection of A097987 and A248150.
Cf. A000010, A000203.

Programs

  • Mathematica
    Do[If[Mod[DivisorSigma[1,n],4]==0 && Mod[EulerPhi[n],4]==2,Print[n]],{n,1,10^3}] (* Vincenzo Librandi, Oct 02 2017 *)
  • PARI
    isok(m) = ((sigma(m) % 4) == 0) && ((eulerphi(m) % 4) == 2); \\ Michel Marcus, Oct 02 2017
  • PARI
    upto(n) = {my(l=List()); forprime(p=3, n, if(p%4==3, forstep(e=1, logint(n,p), 2, listput(l,p^e); if(2*p^e <= n, listput(l,2*p^e))))); listsort(l); l} \\ David A. Corneth, Oct 02 2017

Formula

As 22 = 2 * 11^1, which is of the form 2 * p^k with p = 11 = 2 * 4 + 3 == 3 mod 4 and k = 1 which is odd, 22 is a term. - David A. Corneth, Oct 02 2017
Showing 1-3 of 3 results.

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

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