A135627 Perfect numbers minus 1.

5, 27, 495, 8127, 33550335, 8589869055, 137438691327, 2305843008139952127, 2658455991569831744654692615953842175, 191561942608236107294793378084303638130997321548169215

Offset: 1

Author

Omar E. Pol, Nov 27 2007

Keywords

• nonn

Comments

Conjecture: every odd prime is a factor of at least one number in this sequence. - J. Lowell, Apr 17 2014

a(n) written in base 2 is A138831(n) which is also a member of A138148 (cyclops numbers with binary digits only), assuming there are no odd perfect numbers. - Omar E. Pol, Oct 24 2016 [clarified on Nov 03 2018].

Links

• G. C. Greubel, Table of n, a(n) for n = 1..15

Crossrefs

Cf. A000396, A065091, A138148, A134808, A138831.

Programs

Mathematica

(# (# + 1))/2 & /@ Select[2^Range[100] - 1, PrimeQ] - 1 (* G. C. Greubel, Oct 24 2016, based on Harvey P. Dale code from A000396 *)

Formula

a(n) = A000396(n) - 1.