OFFSET
1,2
COMMENTS
Also row n lists numbers k < p^2 such that the multiplicative order of k modulo p^2 is p - 1.
Row n has phi(prime(n) - 1) = A008330(n) terms.
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.
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?
EXAMPLE
(2) 1,
(3) 8,
(5) 7, 18,
(7) 19, 31,
(11) 40, 94, 112, 118,
(13) 19, 80, 89, 150,
(17) 40, 65, 75, 131, 158, 214, 224, 249,
(19) 116, 127, 262, 299, 307, 333,
(23) 28, 42, 63, 130, 195, 263, 274, 352, 359, 411,
MATHEMATICA
Table[Select[Range[p^2 - 1], MultiplicativeOrder[#, p^2] == p - 1 &], {p, Prime@ Range@ 11}] // Flatten (* Michael De Vlieger, Aug 05 2018 *)
PROG
(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, ", ")))))
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Jianing Song, Aug 05 2018
STATUS
approved