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 A349242 #12 Nov 14 2021 03:30:50
%S A349242 40,56,84,88,104,132,136,152,156,184,198,204,220,228,232,234,248,260,
%T A349242 276,296,297,306,328,340,342,344,348,351,372,376,380,414,424,444,459,
%U A349242 460,472,476,488,492,510,513,516,522,532,536,558,564,568,570,580
%N A349242 Numbers N = pqrs such that |pqr - s| < |ps - qr|, where p <= q <= r <= s are the 4 prime factors of N.
%C A349242 The set A014613 of numbers n with bigomega(n) = A001222(n) = 4, can be partitioned in these here (of "cis" type), and their complement A349241, those of "trans" type; see the math-fun post in LINKS for this suggested terminology.
%C A349242 Within the 4-almost primes below 10^k, k = 2, 3, ...,8, we have (92, 1215, 13784, 148834, 1559299, 16089405, ...) of cis type, more than twice as much as those of trans type.
%H A349242 Marc LeBrun, <a href="https://mailman.xmission.com/hyperkitty/list/math-fun@mailman.xmission.com/message/PTOR2R5FAKLHLW6M2HKKXNXDHTQ4VIUR/">four factor fun</a>, math-fun mailing list (available for subscribers only), Nov 10 2021
%F A349242 { N in A014613 | |g - N/g| < |sg - N/sg| }, where g = gpf(N) = A006530(N) is the greatest, and s = spf(N) = A020639(N) is the smallest prime factor.
%e A349242 The first three 4-almost primes 16 = 2^4, 24 = 2^3*3 and 36 = 2^2*3^2 are not in this sequence, because the factorization u*v with closest possible factors u and v consists of choosing both, u and v, to be semiprimes (namely, 4*4, 4*6 and 6*6).
%e A349242 The 4-almost prime 40 = 2^3*5 is in this sequence because the factorization 40 = u*v with u = 2^3, v = 5 has closer factors (distance 8 - 5 = 3) than u = 2*2, v = 2*5 (distance 10 - 4 = 6).
%o A349242 (PARI) select( {is_A349242(n,a(u)=abs(u-n\u))=bigomega(n)==4 && a((s=factor(n)[,1])[#s])<a(s[1]*s[#s])}, [1..1000])
%o A349242 (Python)
%o A349242 from itertools import chain
%o A349242 from sympy import factorint
%o A349242 def expand(n):
%o A349242 return list(chain.from_iterable([[i[0] for j in range(i[1])] for i in factorint(n).items()]))
%o A349242 def is_ok(p,q,r,s):
%o A349242 return abs(p*q*r - s)<abs(p*s-q*r)
%o A349242 print([i for i in range(2, 1000) if len(expand(i)) == 4 and is_ok(*expand(i))]) #_Gleb Ivanov_, Nov 12 2021
%Y A349242 Cf. A014613, A349241, A006530, A020639.
%K A349242 nonn
%O A349242 1,1
%A A349242 _M. F. Hasler_, Nov 12 2021