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.

A090160 Greater prime factor of semiprimes in A090159.

Original entry on oeis.org

5, 11, 103, 71, 661, 329891, 75024347, 3790360487, 1713311273363831, 117876683047, 765041185860961084291, 38681321803817920159601, 237649652991517758152033, 10513391193507374500051862069, 4379593820587205958191075783529691, 37280713718589679646221
Offset: 1

Views

Author

Ray Chandler, Nov 22 2003

Keywords

Crossrefs

Cf. A038507, A078778, A082952, A090159.

Extensions

Offset changed to 1 and more terms from Jinyuan Wang, Aug 01 2021

A078778 Numbers n such that n!+1 is a semiprime.

Original entry on oeis.org

4, 5, 6, 7, 8, 10, 13, 14, 19, 20, 24, 25, 26, 28, 34, 38, 48, 54, 55, 59, 71, 75, 92, 109, 114, 115
Offset: 1

Views

Author

Jason Earls, Jan 09 2003

Keywords

Comments

Subsequence of (and likely is equal to) the union of A146968 and A181764. - Max Alekseyev, May 28 2015
Note that the two prime factors of 38!+1 = 523022617466601111760007224100074291200000001 = 14029308060317546154181 * 37280713718589679646221 both have 23 decimal digits. Are there any other terms in this sequence other than 4,5,7 and 38 with this property?
a(27) > 139. - Robert Price, Apr 11 2019
Other terms in this sequence: 392, 551, 601, 770, 772, 878, 1033, 1320, 1831, 2620, 2808, 3752, 4233, 4616, 4984, 7260. - Chai Wah Wu, Feb 28 2020

Examples

			4 is in the sequence because 4!+1=25=5*5 is semiprime. But 9 is not in the sequence because 9!+1=19*71*269 is not semiprime. - _Sean A. Irvine_, Nov 15 2009

Links

Crossrefs

Cf. A001358, A082952, A090159, A090160, A078781.

Programs

  • Magma
    IsSemiprime:=func< n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [n: n in [1..60] | IsSemiprime(Factorial(n)+1)]; // Vincenzo Librandi, May 26 2015
  • Mathematica
    Select[Range[100], Plus@@Last/@FactorInteger[#! + 1]==2 &] (* Vincenzo Librandi, May 26 2015 *)
Select[Range[100],PrimeOmega[#!+1]==2&] (* Harvey P. Dale, Mar 19 2017 *)
  • PARI
    { fp(a,b)=local(c,d,r); for(n=a,b,r=n!+1; c=vecmin(factor(r)[, 1]~); d=vecmax(factor(r)[,1]~); if(bigomega(r)==2 && isprime(c) && isprime(d), print1(n" ");)) } fp(1,100)

Extensions

Term 109 from Sean A. Irvine, Nov 15 2009
Term 114 (factored by Womack et al.) from Sean A. Irvine, May 25 2015
Term 115 (factored by Womack et al.) from Sean A. Irvine, Feb 08 2016

A070525 Numbers n such that n-th cyclotomic polynomial evaluated at phi(n) is a prime number.

Original entry on oeis.org

2, 3, 4, 6, 7, 8, 12, 18, 21, 30, 45, 48, 70, 120, 127, 153, 182, 204, 212, 282, 318, 322, 910, 1167, 1177, 1342, 1680, 1963, 2670, 4398, 4655, 8088, 8599, 8808, 19680
Offset: 1

Views

Author

Labos Elemer, May 02 2002

Keywords

Comments

These are probable primes for n > 910. No others for n <= 10000. The prime values of n are 2, 3, 7, 127 and 8599 (A088856). - T. D. Noe, Nov 23 2003
All terms <= 2670, except 1963, have been certified prime with PARI's ECPP. There are no other terms <= 25000. - Lucas A. Brown, Jan 08 2021

Examples

			n=7: Phi(7)=6, Cyclotomic(7,6)=1+6+36+216+1296+7776+46656=55987 is prime.

Links

Crossrefs

Cf. A070518, A070519, A070520, A070521, A070522, A070523, A070524.
Cf. A088856, A090159.

Programs

  • Mathematica
    Do[s=Cyclotomic[n, EulerPhi[n]]; If[PrimeQ[s], Print[n]], {n, 1, 400}]
  • PARI
    isok(n) = isprime(polcyclo(n, eulerphi(n))); \\ Michel Marcus, Sep 01 2019

Extensions

More terms from T. D. Noe, Nov 23 2003
a(35) by Lucas A. Brown, Jan 08 2021
Showing 1-3 of 3 results.

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

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