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A060286 2^(p-1)*(2^p-1) where p is a prime. 4

%I

%S 6,28,496,8128,2096128,33550336,8589869056,137438691328,

%T 35184367894528,144115187807420416,2305843008139952128,

%U 9444732965670570950656,2417851639228158837784576,38685626227663735544086528

%N 2^(p-1)*(2^p-1) where p is a prime.

%C 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

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

%H Harry J. Smith, <a href="/A060286/b060286.txt">Table of n, a(n) for n = 1..100</a>

%F 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

%F a(A016027(n)) = A000396(n), assuming there are no odd perfect numbers. - _Omar E. Pol_, Dec 13 2012

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

%t Table[2^(Prime[n] - 1)(2^Prime[n] - 1), {n, 16}] (* _Alonso del Arte_, Dec 12 2012 *)

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

%Y Cf. A000396, A006516.

%K nonn

%O 1,1

%A _Jason Earls_, Mar 23 2001

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Last modified July 17 08:42 EDT 2019. Contains 325098 sequences. (Running on oeis4.)