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.

A065528 Numbers n such that phi(n) is a nontrivial power b^c where b > 1 and c > 1.

Original entry on oeis.org

5, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 37, 40, 48, 51, 57, 60, 63, 64, 68, 74, 76, 80, 85, 96, 101, 102, 108, 114, 120, 125, 126, 128, 136, 160, 170, 185, 192, 197, 202, 204, 219, 240, 247, 250, 255, 256, 257, 259, 272, 273, 285, 292, 296, 304, 315, 320, 327, 333
Offset: 1

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Author

Joseph L. Pe, Nov 27 2001

Keywords

Comments

What values of b can occur?
Apparently all even numbers can occur as values of b. Checked up to 50000; see A227533. - Charles R Greathouse IV, Jul 15 2013

Examples

			phi(63) = 6^2, phi(96) = 2^5.

Links

Crossrefs

Cf. A166955.

Programs

  • Mathematica
    ppQ[n_] := GCD @@ Last /@ FactorInteger@ n > 1; Select[ Range@ 330, ppQ@ EulerPhi@ # &] (* Robert G. Wilson v, Jul 16 2013 *)
  • PARI
    v=[]; for(n=2, 333, if(ispower(eulerphi(n)), v=concat(v, n))); v (Hobson)
  • PARI
    is(n)=ispower(eulerphi(n)) \\ Charles R Greathouse IV, Jul 15 2013

Formula

a(n) = A166955(n+2). - Juri-Stepan Gerasimov, Oct 25 2009

Extensions

More terms from Nick Hobson, Nov 29 2006
b-file from Charles R Greathouse IV, Mar 25 2010

A227534 Even numbers n such that the least e with n^e a totient is a new record.

Original entry on oeis.org

2, 22, 34, 62, 86, 202, 398, 2042, 6998, 12514, 12758, 33406, 48962, 101554, 154186, 197378, 298366
Offset: 1

Views

Author

Charles R Greathouse IV, Jul 14 2013

Keywords

Comments

Essentially position of records in A227533.
Probably all terms beyond the first are even semiprimes: conjecturally this is a subsequence of A001747.

Crossrefs

Cf. A227533, A227535.

Programs

  • PARI
    r=0;forstep(n=2,1e5,2, t=1; while(!istotient(n^t++),); if(t>r,r=t;print1(n", ")))
\\ See also A227533 for a more efficient method of computing terms.

Extensions

a(14) from Charles R Greathouse IV, Jul 16 2013
a(15) from Charles R Greathouse IV, Jul 17 2013
a(16)-a(17) from Charles R Greathouse IV, Jul 19 2013

A227535 Exponents e such that n^e is the least totient for some even n and all even k < n have a totient of the form k^f for some f < e.

Original entry on oeis.org

2, 3, 4, 5, 15, 17, 23, 42, 44, 47, 68, 80, 107, 130, 142, 162, 184
Offset: 1

Views

Author

Charles R Greathouse IV, Jul 14 2013

Keywords

Comments

Records in A227533.

Crossrefs

Cf. A227533, A227534.

Programs

  • PARI
    r=0;forstep(n=2,1e5,2, t=1; while(!istotient(n^t++),); if(t>r, r=t;print1(t", ")))
\\ See also A227533 for a more efficient method of computing terms.

Formula

a(n) = A227533(A227534(n)/2).

Extensions

a(14) from Charles R Greathouse IV, Jul 16 2013
a(15) from Charles R Greathouse IV, Jul 17 2013
a(16)-a(17) from Charles R Greathouse IV, Jul 19 2013
Showing 1-3 of 3 results.

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

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