VOOZH about

URL: https://oeis.org/A105331

⇱ A105331 - OEIS

login
A105331
Numbers of the form 2^n*(2^(n+1)+2n+1) where 2^(n+1)+2n+1 is prime.
3
3, 14, 52, 184, 656, 34688, 2118656, 134438912, 537346048, 9007202811510784, 2417851639318318791262208, 633825300114170432793740312576, 2535301200456572518883997515776
OFFSET
1,1
COMMENTS
This sequence is a subsequence of A083874 (see A083874 & A105330).
This is because these numbers satisfy tau(n) + sigma(n) = 2n when n = 2^k * p with p is prime; for instance tau(14) + sigma(14) = 4 + 24 = 28 = 2 x 14. [See References.] - Bernard Schott, Apr 07 2017
REFERENCES
J.-M. De Koninck and A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Ellipses, Problème 723, page 93.
FORMULA
a(n) = 2^A105330(n)*(2^(A105330(n)+1) + 2*A105330(n) + 1). - Bernard Schott, Apr 07 2017
EXAMPLE
9007202811510784 is in the sequence because 9007202811510784 = 2^26*(2^27 + 2*26 + 1) and 2^27 + 2*26 + 1 is prime.
MATHEMATICA
Do[If[PrimeQ[2^(m + 1) + 2m + 1], Print[2^m(2^(m + 1) + 2m + 1)]], {m, 0, 110}]
2^# (2^(#+1)+2#+1)&/@Select[Range[0, 100], PrimeQ[2^(#+1)+2#+1]&] (* Harvey P. Dale, Nov 13 2012 *)
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Farideh Firoozbakht, Apr 28 2005
STATUS
approved