A152562 - OEIS

%I #11 Jun 05 2022 08:27:53

%S 2,5,20,104,936,13842,188424,3249576,81239400,2388809736,59720243400

%N Smallest number m such that sigma(m) has exactly n distinct prime factors.

%C a(12) <= 4440632687496. - _Donovan Johnson_, Mar 31 2013

%C From _Daniel Suteu_, May 24 2022: (Start)

%C a(12) <= 2571228006912,

%C a(13) <= 85266458294400,

%C a(14) <= 4638227848902900,

%C a(15) <= 209103527633041800,

%C a(16) <= 10931190635671518600,

%C a(17) <= 545209768960172964900,

%C a(18) <= 34893425213451069753600,

%C a(19) <= 2000640771807316185690000. (End)

%F a(n) <= A153076(n), for n >= 2. - _Daniel Suteu_, May 24 2022

%e a(9) = 81239400; sigma(81239400) = 300690390 = 2*3*5*7*11*13*17*19*31 (9 distinct prime factors).

%o (PARI) v=vector(9); for(m=2, 81239400, n=omega(sigma(m)); if(v[n]==0, v[n]=m; print(n " " v[n]))) /* _Donovan Johnson_, Mar 31 2013 */

%Y Cf. A000203, A001221, A153076.

%K nonn,more

%O 1,1

%A _Donovan Johnson_, Dec 09 2008