A198688 -id:A198688 - cp's OEIS frontend

A024076 a(n) = 7^n - n.

1, 6, 47, 340, 2397, 16802, 117643, 823536, 5764793, 40353598, 282475239, 1977326732, 13841287189, 96889010394, 678223072835, 4747561509928, 33232930569585, 232630513987190, 1628413597910431, 11398895185373124, 79792266297611981, 558545864083283986, 3909821048582988027

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (9,-15,7).

Cf. numbers of the form k^n - n: A000325 (k=2), A024024 (k=3), A024037 (k=4), A024050 (k=5), A024063 (k=6), this sequence (k=7), A024089 (k=8), A024102 (k=9), A024115 (k=10), A024128 (k=11), A024141 (k=12).

Cf. A198688 (first differences).

[7^n-n: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011

I:=[1, 6, 47]; [n le 3 select I[n] else 9*Self(n-1)-15*Self(n-2)+7*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 16 2013

A024076:=n->7^n-n; seq(A024076(n), n=0..30); # Wesley Ivan Hurt, Jan 24 2014

Table[7^n - n, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 3 x + 8 x^2) / ((1 - 7 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *)

a(n)=7^n-n \\ Charles R Greathouse IV, Oct 07 2015

From Vincenzo Librandi, Jun 16 2013: (Start)
G.f.: (1-3*x+8*x^2)/((1-7*x)*(1-x)^2).
a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3). (End)
E.g.f.: exp(x)*(exp(6*x) - x). - Elmo R. Oliveira, Sep 10 2024

A293356 Even integers k such that lambda(sum of even divisors of k) = sum of odd divisors of k.

Original entry on oeis.org

2, 20, 40, 48, 68, 176, 212, 304, 328, 944, 1360, 1712, 1888, 2320, 2344, 2864, 4240, 7120, 7888, 7984, 8448, 8960, 11920, 12032, 14416, 14592, 15536, 17492, 20224, 21520, 23984, 24208, 24592, 25904, 26112, 28160, 29440, 30464, 34560, 35920, 36352, 40528, 41296

Offset: 1

Michel Lagneau, Oct 07 2017

nonn

Or even integers k such that A002322(A146076(k)) = A000593(k).
Observations:
The primes a(n)/4: {5, 17, 53, 4373, 13121, ...} are of the form 2*3^m - 1, m > 0 (A079363).
The primes a(n)/8: {5, 41, 293, 4941257, ...} are of the form 6*7^m - 1, m = 0, 1, ... (primes in A198688).
The set of the primes {a(n)/16} = {3, 11, 19, 59, 107, 179, 499, 971, 1499, 1619, ...} contains the primes of the form 4*3^(2m+1) - 1 = {11, 107, 971, ...}, m = 0, 1, ...

			68 is in the sequence because A002322(A146076(68)) = A002322(108) = 18 and A000593(68) = 18.

Robert Israel, Table of n, a(n) for n = 1..738

Cf. A000593, A000668, A002322, A146076, A281707.

with(numtheory):
for n from 2 by 2 to 10^6 do:
x:=divisors(n):n1:=nops(x):s0:=0:s1:=0:
   for k from 1 to n1 do:
    if type(x[k],even)
     then
     s0:=s0+ x[k]:
     else
     s1:=s1+ x[k]:
    fi:
  od:
    if s1=lambda(s0)
     then
     printf(`%d, `,n):
     else
    fi:
od:

fQ[n_] :=
Block[{d = Divisors@n},
  CarmichaelLambda[Plus @@ Select[d, EvenQ]] ==
Plus @@ Select[d, OddQ]]; Select[2 Range@2000, fQ] (* Robert G. Wilson v, Oct 07 2017 *)

is(n)=if(n%2, return(0)); my(s=valuation(n,2),d=sigma(n>>s)); lcm(znstar(d*(2^(s+1)-2))[2])==d \\ Charles R Greathouse IV, Dec 26 2017

Edited by Robert Israel, Dec 28 2017

cp's OEIS Frontend

A024076 a(n) = 7^n - n.

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