A242389 2^n minus the sum of the proper divisors of n.

2, 3, 7, 13, 31, 58, 127, 249, 508, 1016, 2047, 4080, 8191, 16374, 32759, 65521, 131071, 262123, 524287, 1048554, 2097141, 4194290, 8388607, 16777180, 33554426, 67108848, 134217715, 268435428, 536870911, 1073741782, 2147483647, 4294967265, 8589934577

Offset

1,1

Comments

The primes in the sequence are: 2, 3, 7, 13, 31, 127, 8191, 65521, 131071, 524287, 2147483647,... .

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = A000079(n) - A001065(n).

Example

For n = 4, 2^4 = 16, sum of proper divisors of n is 1 + 2 = 3, so a(4) = 16 - 3 = 13.

Maple

with(numtheory); A242389:=n->2^n+n-sigma(n); seq(A242389(n), n=1..50); # Wesley Ivan Hurt, May 13 2014

Mathematica

Table[2^n + n - DivisorSigma[1, n], {n, 50}] (* Wesley Ivan Hurt, May 13 2014 *)

Prog

(Magma) [2^n + n - DivisorSigma(1, n): n in [1..30]];
(PARI) a(n) = 2^n + n - sigma(n); \\ Michel Marcus, May 13 2014

Crossrefs

Sequence in context: A333313 A262829 A071899 * A102644 A014234 A124430

Adjacent sequences: A242386 A242387 A242388 * A242390 A242391 A242392

Keyword

nonn

Author

Juri-Stepan Gerasimov, May 12 2014.

Extensions

a(30) corrected by Michel Marcus, Jun 14 2022

Status

approved