OFFSET
1,2
COMMENTS
The ratio a(n)/n tends to infinity as n grows (Müller and Schlage-Puchta, 2004).
Decompose (Z/kZ)* as a product of cyclic groups C_{k_1} x C_{k_2} x ... x C_{k_m}, where k_i divides k_j for i < j, then k is a term if and only if m <= 1, or v(k_{m-1},p) < v(k_m,p) holds for all primes p dividing k_m = psi(k), where v(s,p) is the p-adic valuation of s. Otherwise, there are more than phi(phi(k)) residues modulo k of the maximum order. See my Oct 12 2021 formula for A111725 for a proof. - Jianing Song, Oct 20 2021
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Peter J. Cameron and D. A. Preece, Primitive lambda-roots, 2014.
T. W. Müller and J.-C. Schlage-Puchta, On the number of primitive lambda-roots, Acta Arithmetica, Vol. 115 (2004), pp. 217-223.
MATHEMATICA
q[n_] := Count[(t = Table[MultiplicativeOrder[k, n], {k, Select[Range[n], CoprimeQ[n, #] &]}]), Max[t]] == EulerPhi[EulerPhi[n]]; Select[Range[100], q] (* Amiram Eldar, Oct 12 2021 *)
PROG
(PARI) isA300064(n) = my(v=znstar(n)[2], l=#v); if(l<2, return(1), my(U=v[1], L=v[2], d=factor(U), w=omega(U)); for(i=1, w, if(valuation(L, d[i, 1]) == d[i, 2], return(0))); return(1)) \\ Jianing Song, Oct 20 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Max Alekseyev, Feb 23 2018
STATUS
approved