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 A386572 #6 Jul 30 2025 00:54:13
%S A386572 3,11,14,21,26,29,34,35,38,45,48,51,54,57,59,61,62,64,68,69,71,74,76,
%T A386572 79,81,87,94,97,98,101,105,110,118,123,124,125,129,133,134,137,142,
%U A386572 147,149,155,158,160,165,170,173,174,177,182,184,186,188,189,191,193,197
%N A386572 Numbers that are not of the form k - Omega(k), where Omega(k) is the number of prime factors of k counted with multiplicity.
%C A386572 Luca (2005) proved that this sequence is infinite, and Kátai (2006) proved that it has a positive lower density.
%H A386572 Amiram Eldar, <a href="/A386572/b386572.txt">Table of n, a(n) for n = 1..10000</a>
%H A386572 Imre Kátai, <a href="https://doi.org/10.1007/s10474-006-0107-8">A remark on a paper of Luca</a>, Acta Mathematica Hungarica, Vol. 113, No. 4 (2006), pp. 313-318.
%H A386572 Florian Luca, <a href="https://doi.org/10.1007/s10474-005-0010-8">On numbers not of the form n-omega(n)</a>, Acta Mathematica Hungarica, Vol. 106, No. 1 (2005), pp. 117-135.
%t A386572 seq[lim_] := Complement[Range[lim], Table[k - PrimeOmega[k], {k, 1, lim + Log2[lim]}]]; seq[200]
%o A386572 (PARI) list(lim) = setminus(vector(lim, i, i), Set(vector(lim + logint(lim, 2), i, i - bigomega(i))));
%Y A386572 Cf. A001222, A069345.
%Y A386572 Numbers not of the form k-f(k): A005278 (phi), A045765 (d), A386571 (omega), this sequence (Omega).
%K A386572 nonn
%O A386572 1,1
%A A386572 _Amiram Eldar_, Jul 26 2025