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

1,1

Comments

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

Links

Table of n, a(n) for n=1..27.

Example

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.

Prog

(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)

Crossrefs

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

Sequence in context: A291548 A212019 A075708 * A272272 A024589 A062015

Adjacent sequences: A066614 A066615 A066616 * A066618 A066619 A066620

Keyword

nonn

Author

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

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

Status

approved