login
A242441
Numbers n such that there are no integer k < sqrt(n) and prime p < n with k^2*p == 1 (mod n).
4
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 18, 20, 21, 24, 28, 30, 32, 39, 40, 48, 50, 56, 60, 63, 70, 72, 80, 88, 102, 110, 112, 120, 126, 156, 168, 204, 213, 220, 232, 240, 252, 272, 273, 280, 312, 372, 378, 408, 520, 527, 546, 760, 765, 780, 813, 840, 968, 1320, 1715, 1848
OFFSET
1,2
COMMENTS
Conjecture: The sequence only has 61 terms as listed.
We have checked this extension of the conjecture in A242425 for n up to 10^7.
LINKS
EXAMPLE
a(5) = 5 since none of 1^2*2 = 2, 1^2*3 = 3, 2^2*2 = 8 and 2^2*3 = 12 is congruent to 1 modulo 5.
MATHEMATICA
r[k_, n_]:=r[k, n]=PowerMod[k^2, -1, n]
m=0; Do[Do[If[GCD[k, n]==1&&PrimeQ[r[k, n]], Goto[aa]], {k, 1, Sqrt[n-1]}]; m=m+1; Print[m, " ", n]; Label[aa]; Continue, {n, 1, 2000}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 14 2014
STATUS
approved