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 A373467 #11 Jun 07 2024 08:05:23
%S A373467 20522502,21033012,22444422,23555532,24266242,25777752,26588562,
%T A373467 35888853,36399363,41555514,41855814,42066024,43477434,43777734,
%U A373467 44888844,45999954,47199174,51066015,51666615,52777725,53588535,53888835,55233255,59911995,60066006,60366306,61777716,62588526,62700726
%N A373467 Palindromes with exactly 7 (distinct) prime divisors.
%F A373467 Intersection of A002113 and A176655.
%e A373467 Obviously all terms must be palindromic; let us consider the prime factorization:
%e A373467 a(1) = 20522502 = 2 * 3^2 * 7 * 11 * 13 * 17 * 67 has exactly 7 distinct prime divisors, although the factor 3 appears twice in the factorization. (Without the second factor 3 the number would not be palindromic.)
%e A373467 a(2) = 21033012 = 2^2 * 3 * 7 * 11 * 13 * 17 * 103 has exactly 7 distinct prime divisors, although the factor 2 appears twice in the factorization. (Without the second factor 2 the number would not be palindromic.)
%e A373467 a(3) = 22444422 = 2 * 3 * 7 * 11 * 13 * 37 * 101 is the product of 7 distinct primes (cf. A123321), hence the first squarefree term of this sequence.
%o A373467 (PARI) A373467_upto(N, start=vecprod(primes(7)), num_fact=7)={ my(L=List()); while(N >= start = nxt_A002113(start), omega(start)==num_fact && listput(L, start)); L}
%Y A373467 Cf. A046333 (same with bigomega = 7: counting prime factors with multiplicity), A046397 (same but only squarefree terms), A373465 (same with omega = 5), A046396 (same with omega = 6).
%Y A373467 Cf. A002113 (palindromes), A176655 (omega(.) = 7), A123321 (products of 7 distinct primes).
%K A373467 nonn,base
%O A373467 1,1
%A A373467 _M. F. Hasler_, Jun 06 2024