A121290 -id:A121290 - cp's OEIS frontend

A060286 a(n) = 2^(p-1)*(2^p-1) where p is prime(n).

6, 28, 496, 8128, 2096128, 33550336, 8589869056, 137438691328, 35184367894528, 144115187807420416, 2305843008139952128, 9444732965670570950656, 2417851639228158837784576, 38685626227663735544086528, 9903520314282971830448816128, 40564819207303336344294875201536

Offset: 1

Jason Earls, Mar 23 2001

nonn

a(n) is the number whose binary representation is p 1's together with p-1 0's, where p is prime(n), for example: prime(3) = 5 so a(3) = 496 = 111110000 (2). - Omar E. Pol, Dec 12 2012

			a(4) = 2^6(2^7 - 1) = 8128.

C. Stanley Ogilvy and John T. Anderson, "Excursions in Number Theory", Oxford University Press, NY, 1966 pp. 20-23.

Harry J. Smith, Table of n, a(n) for n = 1..100

Cf. A000040, A000396, A006516.

Table[2^(Prime[n] - 1)(2^Prime[n] - 1), {n, 16}] (* Alonso del Arte, Dec 12 2012 *)

{ n=0; forprime (p=1, 542, write("b060286.txt", n++, " ", 2^(p - 1)*(2^p - 1)); ) } \\ Harry J. Smith, Jul 03 2009

For n > 1, a(2n) = 9*T(k) + 1 ; a(2n+1) = 9*T(K) + 1, where T(n) = A000217(n), k = (A121290(n) - 1)/2, K = 2*A121290(n). - Lekraj Beedassy, Sep 12 2006

a(A016027(n)) = A000396(n), assuming there are no odd perfect numbers. - Omar E. Pol, Dec 13 2012

A173588 T(n,k) = (k^n)*U(n, (1/k + k)/2), where U(n,x) is the n-th Chebyshev polynomial of the second kind, square array read by antidiagonals upward (n >= 0, k >= 1).

Original entry on oeis.org

1, 2, 1, 3, 5, 1, 4, 21, 10, 1, 5, 85, 91, 17, 1, 6, 341, 820, 273, 26, 1, 7, 1365, 7381, 4369, 651, 37, 1, 8, 5461, 66430, 69905, 16276, 1333, 50, 1, 9, 21845, 597871, 1118481, 406901, 47989, 2451, 65, 1, 10, 87381, 5380840, 17895697, 10172526, 1727605, 120100, 4161, 82, 1

Offset: 0

Roger L. Bagula, Feb 22 2010

The intersection of this sequence and A121290 is the sequence 1, 5, 85, 341, 5461, 21845, .... - Paul Muljadi, Jan 27 2011

			Square array begins:
  n\k | 1    2      3        4         5          6 ...
  -----------------------------------------------------
   0  | 1    1      1        1         1          1 ...
   1  | 2    5     10       17        26         37 ...
   2  | 3   21     91      273       651       1333 ...
   3  | 4   85    820     4369     16276      47989 ...
   4  | 5  341   7381    69905    406901    1727605 ...
   5  | 6 1365  66430  1118481  10172526   62193781 ...
   6  | 7 5461 597871 17895697 254313151 2238976117 ...
   ...

Cf. A001045, A002450.

Cf. A173590, A173591.

p[x_, q_] = 1/(x^2 - (1/q + q)*x + 1);
a = Table[Table[n^m*SeriesCoefficient[Series[p[x, n], {x, 0, 50}], m], {m, 0, 20}], {n, 1, 21}];
Flatten[Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}]]

T(n, k) := k^n*chebyshev_u(n, (1/k + k)/2)$
create_list(T(n - k + 1, k), n, 0, 12, k, 1, n + 1);
/* Franck Maminirina Ramaharo, Jan 18 2019 */

T(n,k) = (k^n)*([x^n] 1/(x^2 - (1/k + k)*x + 1)).

Edited by Franck Maminirina Ramaharo, Jan 24 2019

cp's OEIS Frontend

A060286 a(n) = 2^(p-1)*(2^p-1) where p is prime(n).

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