A152562 Smallest number m such that sigma(m) has exactly n distinct prime factors.

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

Offset: 1

Author

Donovan Johnson, Dec 09 2008

Keywords

• nonn
• more

Comments

a(12) <= 4440632687496. - Donovan Johnson, Mar 31 2013

From Daniel Suteu, May 24 2022: (Start)

a(12) <= 2571228006912,

a(13) <= 85266458294400,

a(14) <= 4638227848902900,

a(15) <= 209103527633041800,

a(16) <= 10931190635671518600,

a(17) <= 545209768960172964900,

a(18) <= 34893425213451069753600,

a(19) <= 2000640771807316185690000. (End)

Examples

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

Crossrefs

Cf. A000203, A001221, A153076.

Programs

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 */

Formula

a(n) <= A153076(n), for n >= 2. - Daniel Suteu, May 24 2022