This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382120 #23 May 30 2025 23:15:22
%S A382120 10,18,20,21,22,26,28,30,34,36,38,40,42,46,48,50,52,54,55,57,58,60,68,
%T A382120 72,74,78,82,84,86,93,94,96,98,100,106,108,110,111,114,116,117,118,
%U A382120 122,124,126,129,132,134,136,142,146,147,148,150,156,158,162,164,165
%N A382120 Numbers k in A024619 such that there exists a prime p | k for which p^(m+1) == r (mod k), where r is also in A024619, and a prime q | k for which q^(m+1) == r (mod k), where r is a prime power.
%C A382120 This sequence intersects neither A381750 nor A381864.
%H A382120 Michael De Vlieger, <a href="/A382120/b382120.txt">Table of n, a(n) for n = 1..10000</a>
%e A382120 Table of a(n) for select n, 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.
%e A382120 p_x^(m+1) mod n
%e A382120 n a(n) facs(a(n)) p_1 p_2 p_3
%e A382120 -----------------------------------------
%e A382120 1 10 2 * 5 [6] 5
%e A382120 2 18 2 * 3^2 [14] 9
%e A382120 3 20 2^2 * 5 [12] 5
%e A382120 4 21 3 * 7 [6] 7
%e A382120 5 22 2 * 11 [10] 11
%e A382120 6 26 2 * 13 [6] 13
%e A382120 7 28 2^2 * 7 4 [21]
%e A382120 8 30 2 * 3 * 5 2 [21] 5
%e A382120 9 34 2 * 17 [30] 17
%e A382120 10 36 2^2 * 3^2 [28] 9
%e A382120 11 38 2 * 19 [26] 19
%e A382120 22 60 2^2 * 3 * 5 4 [21] 5
%t A382120 nn = 165, Reap[Do[If[! PrimePowerQ[n], If[CountDistinct@ Map[Boole@ PrimePowerQ@ PowerMod[#, 1 + Floor@ Log[#, n], n] &, FactorInteger[n][[All, 1]] ] == 2, Sow[n]]], {n, 2, nn}] ][[-1, 1]]
%Y A382120 Cf. A000961, A024619, A381750, A381864.
%K A382120 nonn
%O A382120 1,1
%A A382120 _Michael De Vlieger_, Apr 06 2025