A143422 -id:A143422 - cp's OEIS frontend

A143421 Number of odd numbers k such that phi(k) = n, where n runs through the values (A002202) taken by phi.

1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 3, 1, 1, 1, 3, 3, 2, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 1, 6, 1, 2, 1, 2, 2, 1, 4, 2, 1, 1, 1, 4, 1, 2, 1, 6, 1, 1, 1, 3, 1, 1, 1, 5, 1, 1, 3, 2, 2, 1, 1, 4, 1, 2, 1, 5, 1, 1, 4, 1, 1, 3, 1, 1, 1, 1, 7, 2, 1, 2, 1, 1, 2, 1, 10, 1, 4, 1, 1, 1, 3, 1, 1, 2, 4, 3, 1, 6, 1, 1, 1, 2, 1, 1, 6

Offset: 1

T. D. Noe, Aug 14 2008

nonn

The first zero term is for n = 16842752 = 257*2^16. If there are only five Fermat primes, then terms will be zero for n=2^r for all r>31. This is discussed in problem E3361.

a(2698482) = 0. That is, the 2698482nd term of A002202 is 16842752. - T. D. Noe, Aug 19 2008

R. K. Guy, Unsolved problems in number theory, B39.

T. D. Noe, Table of n, a(n) for n=1..10000
T. D. Noe, Numbers Like 16842752
William P. Wardlaw, L. L. Foster and R. J. Simpson, Problem E3361, Amer. Math. Monthly, Vol. 98, No. 5 (May, 1991), 443-444.

A058277(n) = A143421(n) + A143422(n).

A207335 Number of minimal polynomials of 2*cos(Pi/N) with allowed degree given by A207333.

Original entry on oeis.org

3, 3, 2, 4, 1, 4, 5, 2, 3, 1, 7, 1, 1, 6, 5, 6, 2, 2, 1, 9, 1, 1, 2, 1, 5, 7, 1, 1, 11, 1, 8, 1, 4, 4, 2, 13, 2, 1, 2, 1, 5, 1, 4, 2, 11, 1, 8, 1, 4, 1, 1, 2, 16, 1, 1, 4, 10

Offset: 1

Wolfdieter Lang, Feb 19 2012

For the minimal polynomials C(N,x) of 2*cos(Pi/N) with degree delta(N) see A207333.

			a(8)=2 because there are exactly 2 values of N, namely 19 and 27 (see row no. 7 of the array A207334), for which the minimal polynomial C(N,x) has degree delta(N) = A207333(8) = 9.

Cf. A207333, A143422.

a(n) is the number of different indices N of minimal polynomials C(N,x) of 2*cos(Pi/N) with allowed degree delta(N)=A207333(n), n>=1.

cp's OEIS Frontend

A143421 Number of odd numbers k such that phi(k) = n, where n runs through the values (A002202) taken by phi.

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