A088856 -id:A088856 - cp's OEIS frontend

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

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

Labos Elemer, May 02 2002

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

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

Lucas A. Brown, A070525.py.

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

Cf. A088856, A090159.

Do[s=Cyclotomic[n, EulerPhi[n]]; If[PrimeQ[s], Print[n]], {n, 1, 400}]

isok(n) = isprime(polcyclo(n, eulerphi(n))); \\ Michel Marcus, Sep 01 2019

More terms from T. D. Noe, Nov 23 2003

a(35) by Lucas A. Brown, Jan 08 2021

A101753 Numbers m such that Sum_{k=0..m} m^k is prime.

Original entry on oeis.org

1, 2, 6, 126, 8598

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Dec 15 2004

Value of sum for m = 126 has been checked to be probably prime with the isprime functions of PARI and Maple V. Also checked with ECM - see link.
Note that m+1 must be prime and hence a(n) = A088856(n) - 1. Another way to compute the number is (m^(m + 1) - 1)/(m - 1). - T. D. Noe, Dec 15 2004
Value of sum for m = 126 has been certified prime with Primo. - Ryan Propper, Jul 11 2005

			The number 6 is in this sequence because 6^0 + 6^1 + 6^2 + 6^3 + 6^4 + 6^5 + 6^6 = (6^7 - 1)/5 = 55987 is prime.

Dario Alpern, Integer factorization calculator.

Cf. A031973.

Cf. A088856 (primes p such that cyclotomic(p,p-1) is prime).

a(n) = A088856(n) - 1.

One more term from T. D. Noe, Dec 15 2004

Edited by Thomas Ordowski, Sep 02 2021

cp's OEIS Frontend

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

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