A070175 The smallest representative of each (bigomega(n),omega(n)) pair.

1, 2, 4, 6, 8, 12, 16, 24, 30, 32, 48, 60, 64, 96, 120, 128, 192, 210, 240, 256, 384, 420, 480, 512, 768, 840, 960, 1024, 1536, 1680, 1920, 2048, 2310, 3072, 3360, 3840, 4096, 4620, 6144, 6720, 7680, 8192, 9240, 12288, 13440, 15360, 16384, 18480, 24576

Offset: 0

Author

Rick L. Shepherd, May 06 2002

Keywords

• nonn

Comments

Equivalently, products of a member of A000079 and a member of A002110. - Matthew Vandermast, Nov 04 2008

These are all the numbers of least prime signature (A025487) that are not divisible by 9. - Hal M. Switkay, Jun 23 2025

Examples

			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).
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10186 (all terms a(n) <= A002110(54))

Crossrefs

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

Cf. A025487.

Programs

Mathematica

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 *)

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