A381864 Numbers k in A024619 such that p^(m+1) == r (mod k) where r is also in A024619 for all p | n.
15, 33, 35, 44, 45, 51, 63, 65, 66, 69, 70, 75, 76, 77, 80, 85, 87, 88, 90, 91, 92, 95, 99, 102, 104, 105, 115, 119, 123, 130, 133, 135, 138, 140, 141, 143, 144, 145, 152, 153, 154, 159, 160, 161, 170, 172, 174, 175, 176, 177, 180, 184, 185, 187, 188, 189, 190
Offset: 1
Keywords
Examples
Table of a(n) for n = 1..12, showing prime decomposition (facs(a(n))), p_x^(m+1) mod n, where x = 1 denotes the smallest prime factor, x = 2, the second smallest prime factor, etc. Brackets appear around residues that are not prime powers.
p_x^(m+1) mod n
n a(n) facs(a(n)) p_1 p_2 p_3
-----------------------------------------
1 15 3 * 5 12 10
2 33 3 * 11 15 22
3 35 5 * 7 20 14
4 44 2^2 * 11 20 33
5 45 3^2 * 5 36 35
6 51 3 * 17 30 34
7 63 3^2 * 7 18 28
8 65 5 * 13 60 39
9 66 2 * 3 * 11 62 15 55
10 69 3 * 23 12 46
11 70 2 * 5 * 7 58 55 63
12 75 3 * 5^2 6 50
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
nn = 190, Reap[Do[If[! PrimePowerQ[n], If[NoneTrue[Map[PowerMod[#, 1 + Floor@ Log[#, n], n] &, FactorInteger[n][[All, 1]] ], PrimePowerQ], Sow[n]]], {n, 2, nn}] ][[-1, 1]]
Comments