A103291 Numbers k such that sigma(2^k-1) >= 2*(2^k-1)-1, i.e., the number 2^k-1 is perfect, abundant, or least deficient.

1, 12, 24, 36, 40, 48, 60, 72, 80, 84, 90, 96, 108, 120, 132, 140, 144, 156, 160, 168, 180, 192, 200, 204, 210, 216, 220, 228, 240, 252, 264, 270, 276, 280, 288, 300, 312, 320, 324, 330, 336, 348, 360, 372, 384, 396, 400, 408, 420, 432, 440, 444, 450, 456, 468

Offset: 1

Author

Max Alekseyev, Jan 28 2005

Keywords

• hard
• nonn

Comments

Is there an odd term besides 1? Numbers 2^a(i)-1 form set difference of sequences A103289 and A096399.

Odd terms > 1 exist, but there are none < 10^7. If k > 1 is an odd term, then 2^k-1 must have more than 900000 distinct prime factors and all of them must be members of A014663. - David Wasserman, Apr 15 2008

Links

• Amiram Eldar, Table of n, a(n) for n = 1..136

Crossrefs

Cf. A000203, A075708, A103288, A103289, A103292, A023196.

Programs

PARI

for(i=1,1000,n=2^i-1;if(sigma(n)>=2*n-1,print1(i, ", ")));

Formula

Numbers k such that 2^k-1 is in A103288.

Extensions

More terms from David Wasserman, Apr 15 2008