A070175 - OEIS

%I #17 Oct 09 2024 04:34:50

%S 1,2,4,6,8,12,16,24,30,32,48,60,64,96,120,128,192,210,240,256,384,420,

%T 480,512,768,840,960,1024,1536,1680,1920,2048,2310,3072,3360,3840,

%U 4096,4620,6144,6720,7680,8192,9240,12288,13440,15360,16384,18480,24576

%N The smallest representative of each (bigomega(n),omega(n)) pair.

%C Equivalently, products of a member of A000079 and a member of A002110. - _Matthew Vandermast_, Nov 04 2008

%H 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 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 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 (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 Cf. A001222 (bigomega(n)), A001221 (omega(n)).

%Y Cf. A025487.

%K nonn

%O 0,2

%A _Rick L. Shepherd_, May 06 2002