cp's OEIS Frontend

A317706 Irregular triangle of numbers k < p^2 such that k is a primitive root modulo p but not p^2, p = prime(n).

%I A317706 #13 Aug 28 2018 04:22:19
%S A317706 1,8,7,18,19,31,40,94,112,118,19,80,89,150,40,65,75,131,158,214,224,
%T A317706 249,116,127,262,299,307,333,28,42,63,130,195,263,274,352,359,411,14,
%U A317706 60,137,221,374,416,425,467,620,704,781,827,115,117,145,229,414,513,623,726
%N A317706 Irregular triangle of numbers k < p^2 such that k is a primitive root modulo p but not p^2, p = prime(n).
%C A317706 Also row n lists numbers k < p^2 such that the multiplicative order of k modulo p^2 is p - 1.
%C A317706 Row n has phi(prime(n) - 1) = A008330(n) terms.
%C A317706 Row sum is congruent to mu(prime(n) - 1) = A089451(n) modulo prime(n)^2, where mu is the Moebius function. For n >= 3, the product of n-th row is congruent to 1 modulo prime(n)^2.
%C A317706 Does every integer appear in this sequence? For example, 3 does not appear until the prime 1006003 and 5 does not appear until the prime 40487. Where does 2 first appear?
%e A317706 (2)   1,
%e A317706 (3)   8,
%e A317706 (5)   7, 18,
%e A317706 (7)   19, 31,
%e A317706 (11)  40, 94, 112, 118,
%e A317706 (13)  19, 80, 89, 150,
%e A317706 (17)  40, 65, 75, 131, 158, 214, 224, 249,
%e A317706 (19)  116, 127, 262, 299, 307, 333,
%e A317706 (23)  28, 42, 63, 130, 195, 263, 274, 352, 359, 411,
%t A317706 Table[Select[Range[p^2 - 1], MultiplicativeOrder[#, p^2] == p - 1 &], {p, Prime@ Range@ 11}] // Flatten (* _Michael De Vlieger_, Aug 05 2018 *)
%o A317706 (PARI) forprime(p=2,100,for(i=1,p^2,if(Mod(i,p)!=0,if(znorder(Mod(i,p^2))==p-1,print1(i, ", ")))))
%Y A317706 Cf. A008330, A055578, A089451, A143548.
%K A317706 nonn,tabf
%O A317706 1,2
%A A317706 _Jianing Song_, Aug 05 2018