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

1,2

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

Table of n, a(n) for n=1..55.

Formula

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

Prog

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

Crossrefs

Cf. A103288, A103289, A103292, A023196.

Sequence in context: A009185 A102308 A354583 * A103292 A359565 A335147

Adjacent sequences: A103288 A103289 A103290 * A103292 A103293 A103294

Keyword

hard,nonn

Author

Max Alekseyev, Jan 28 2005

Extensions

More terms from David Wasserman, Apr 15 2008

Status

approved