A066617 Composites of form prime+1 containing a record number of prime factors.

4, 8, 24, 32, 128, 384, 1152, 3584, 5120, 6144, 8192, 73728, 131072, 524288, 5505024, 10616832, 14680064, 18874368, 109051904, 169869312, 654311424, 738197504, 2147483648, 21474836480, 51539607552, 824633720832, 3710851743744

Offset: 1

Author

G. L. Honaker, Jr., Jan 13 2002

Keywords

• nonn

Comments

The sequence contains all numbers of the form (Mersenne Prime)+1 as a subset. - Hugo Pfoertner, Sep 10 2004

Examples

			a(19)=109051904=13*2^23: 24 prime factors, a(20)=169869312=3^4*2^21: 25 prime factors, a(21)=654311424=13*3*2^24: 26 prime factors. a(19)-1, a(20)-1 and a(21)-1 are primes.
		

Crossrefs

Cf. Mersenne Primes + 1: A072868(n)=A000668(n)+1.

Programs

PARI

{A066617(a, b) = local(p, c, d); forprime(p=a,b,d=bigomega(p+1); if(d>c,c=d; print1(p+1,",")))} A066617(3,10^7)

Extensions

More terms from Jason Earls, Jan 15 2002

More terms from Hugo Pfoertner, Sep 10 2004

a(24)-a(27) from Donovan Johnson, Dec 08 2009