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 A070175 #21 Jun 24 2025 18:48:44
%S A070175 1,2,4,6,8,12,16,24,30,32,48,60,64,96,120,128,192,210,240,256,384,420,
%T A070175 480,512,768,840,960,1024,1536,1680,1920,2048,2310,3072,3360,3840,
%U A070175 4096,4620,6144,6720,7680,8192,9240,12288,13440,15360,16384,18480,24576
%N A070175 The smallest representative of each (bigomega(n),omega(n)) pair.
%C A070175 Equivalently, products of a member of A000079 and a member of A002110. - _Matthew Vandermast_, Nov 04 2008
%C A070175 These are all the numbers of least prime signature (A025487) that are not divisible by 9. - _Hal M. Switkay_, Jun 23 2025
%H A070175 Michael De Vlieger, <a href="/A070175/b070175.txt">Table of n, a(n) for n = 0..10186</a> (all terms a(n) <= A002110(54))
%e A070175 24 is a term because (bigomega(24),omega(24))=(4,2) and 24 is the smallest n for which (bigomega(n),omega(n))=(4,2).
%t A070175 f[x_] := Block[{i, k, m, nn, p}, nn = Product[Prime[j], {j, x}]; Set[{k, i, p}, Range[0, 2]]; {1}~Join~Union@ Reap[Until[i > x, While[Set[m, 2^k*p] <= nn, Sow[m]; k++]; k = 0; i++; p *= Prime[i] ] ][[-1, 1]] ]; f[6] (* _Michael De Vlieger_, Oct 08 2024 *)
%o A070175 (PARI) c_max=65; b=vector(c_max); o=vector(c_max); n=1; v=[n]; c=1; first term = 1 b[1] && o[1] are bigomega(1) && omega(1) - already initialized to 0 above. c_max is the total number of terms sought (including 1). Code exits for-loop to try new n upon the first match of a previous pair. until(c==c_max, n++; for(m=1,c, if(bigomega(n)==b[m] && omega(n)==o[m], break, else, if last previous pair checked, save term, save new unique pair if(m==c, v=concat(v,n); c++; b[c]=bigomega(n); o[c]=omega(n))))); v
%Y A070175 Cf. A001222 (bigomega(n)), A001221 (omega(n)).
%Y A070175 Cf. A025487.
%K A070175 nonn
%O A070175 0,2
%A A070175 _Rick L. Shepherd_, May 06 2002