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

0,2

Comments

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

Links

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

Example

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).

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 *)

Prog

(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

Crossrefs

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

Cf. A025487.

Sequence in context: A279537 A325238 A344385 * A096850 A250270 A062847

Adjacent sequences: A070172 A070173 A070174 * A070176 A070177 A070178

Keyword

nonn

Author

Rick L. Shepherd, May 06 2002

Status

approved