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 A373466 #18 Jun 24 2024 10:50:56
%S A373466 222222,282282,414414,444444,474474,555555,606606,636636,646646,
%T A373466 666666,696696,828828,888888,969969,2040402,2065602,2141412,2206022,
%U A373466 2343432,2417142,2444442,2572752,2646462,2673762,2747472,2848482,2875782,2949492,2976792
%N A373466 Palindromes with exactly 6 distinct prime divisors.
%C A373466 The term "exactly" clarifies that we don't mean "at least". But the prime divisors may occur to higher powers in the factorization, cf. Examples.
%C A373466 This is different from A046396 which excludes nonsquarefree terms, i.e., terms where one or more of the distinct prime factors occur to a power greater than 1, as it is possible here, cf. Examples.
%F A373466 Intersection of A002113 and A074969.
%e A373466 a(1) = 222222 = 2 * 3 * 7 * 11 * 13 * 37 has exactly 6 distinct prime divisors.
%e A373466 a(3) = 414414 = 2 * 3^2 * 7 * 11 * 13 * 23 has 6 distinct prime divisors, even though the factor 3 occurs twice in the factorization.
%t A373466 Select[Range[3000000],PalindromeQ[#]&&Length[FactorInteger[#]]==6&] (* _James C. McMahon_, Jun 08 2024 *)
%o A373466 (PARI) A373466_upto(N, start=1, num_fact=6)={ my(L=List()); while(N >= start = nxt_A002113(start), omega(start)==num_fact && listput(L, start)); L}
%Y A373466 Cf. A002113 (palindromes), A074969 (omega(.) = 6).
%Y A373466 Cf. A046332 (same with bigomega = 6: prime factors counted with multiplicity), A046396 (similar, but squarefree terms only), A373465 (same with omega = 5), A373467 (same with bigomega = 7).
%K A373466 nonn,base
%O A373466 1,1
%A A373466 _M. F. Hasler_, Jun 06 2024