

A250201


Least b such that Phi_n(b, b1) is prime.


2



2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 3, 2, 3, 4, 2, 6, 2, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2, 4, 5, 40, 2, 3, 2, 7, 2, 5, 3, 3, 2, 13, 3, 2, 14, 4, 22, 3, 3, 13, 2, 34, 5, 3, 5, 2, 2, 34, 9, 2, 17, 7, 3, 2, 3, 18, 9, 47, 4, 20, 3, 2, 2, 8, 2, 4, 17, 6, 14, 2, 2, 61, 18, 2, 2
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OFFSET

2,1


COMMENTS

Phi_n(b, b1) = (b1)^EulerPhi(n) * Phi_n(b/(b1)).
This sequence is not defined at n = 1 since Phi_1(b, b1) = 1 for all b, and 1 is not prime. Conjecture: a(n) is defined for all n>1.
If b = 1, then Phi_n(b, b1) = 1 for all n, and 1 is not prime, so all a(n) > 1.
a(n) = 2 if and only if n is in A072226.
n Phi_n(a, b)
1 ab
2 a+b
3 a^2+ab+b^2
4 a^2+b^2
5 a^4+a^3*b+a^2*b^2+a*b^3+b^4
6 a^2ab+b^2
... ...
n b^EulerPhi(n)*Phi_n(a/b)


LINKS



EXAMPLE

a(11) = 6 because Phi_11(b, b1) is composite for b = 2, 3, 4, 5 and prime for b = 6.
a(37) = 40 because Phi_37(b, b1) is composite for b = 2, 3, 4, ..., 39 and prime for b = 40.


MATHEMATICA

Table[k = 2; While[!PrimeQ[(k1)^EulerPhi(n)*Cyclotomic[n, k/(k1)]], k++]; k, {n, 2, 300}]


PROG

a(n) = for(k = 2, 2^16, if(ispseudoprime((k1)^eulerphi(n) * polcyclo(n, k/(k1))), return(k)))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



