A078303 -id:A078303 - cp's OEIS frontend

A155877 Sums of three Fermat numbers.

9, 11, 13, 15, 23, 25, 27, 37, 39, 51, 263, 265, 267, 277, 279, 291, 517, 519, 531, 771, 65543, 65545, 65547, 65557, 65559, 65571, 65797, 65799, 65811, 66051, 131077, 131079, 131091, 131331, 196611, 4294967303, 4294967305, 4294967307

Offset: 1

Jonathan Vos Post, Jan 29 2009

nonn

			a(1) = 3 + 3 + 3 = 9.
a(2) = 3 + 3 + 5 = 11.
a(3) = 3 + 5 + 5 = 13.
a(4) = 5 + 5 + 5 = 15.
a(5) = 3 + 3 + 17 = 23.
a(6) = 3 + 5 + 17 = 25.
a(7) = 5 + 5 + 17 = 27.
a(8) = 3 + 17 + 17 = 37.
a(9) = 5 + 17 + 17 = 39.
a(10) = 17 + 17 + 17 = 51.
a(11) = 3 + 3 + 257 = 263.

Eric Weisstein's World of Mathematics, Generalized Fermat Number.

Cf. A000215, A019434, A050922, A051179, A059919, A063486, A073617, A078303, A078304, A085866.

{(2^(2^a) + 1) + (2^(2^b) + 1) + (2^(2^c) + 1)} = {A000215(a) + A000215(b) + A000215(c)}.

More terms from R. J. Mathar, Feb 06 2009

A275379 Number of prime factors (with multiplicity) of generalized Fermat number 6^(2^n) + 1.

Original entry on oeis.org

1, 1, 1, 2, 3, 3, 3, 7, 3, 5

Offset: 0

Arkadiusz Wesolowski, Jul 25 2016

			b(n) = 6^(2^n) + 1.
Complete Factorizations
b(0) = 7
b(1) = 37
b(2) = 1297
b(3) = 17*98801
b(4) = 353*1697*4709377
b(5) = 2753*145601*19854979505843329
b(6) = 4926056449*447183309836853377*28753787197056661026689
b(7) = 257*763649*50307329*3191106049*2339340566463317436161*
       2983028405608735541756929*18247770097021321924017185281
b(8) = 18433*
       69615986569139423375849495295909549956813828853888948633601*P137
b(9) = 80897*3360769*12581314681802812884728041373153281*
       3513902440204553274892072241244613302018049*P311

Cf. A078303, A273947.

Table[PrimeOmega[6^(2^n) + 1], {n, 0, 6}] (* Michael De Vlieger, Jul 26 2016 *)

PARI
```
a(n) = bigomega(factor(6^(2^n)+1))
```

a(n) = A001222(A078303(n)). - Felix Fröhlich, Jul 25 2016

a(8) was found in 2001 by Robert Silverman

a(9) was found in 2007 by Nestor de Araújo Melo

cp's OEIS Frontend

A155877 Sums of three Fermat numbers.

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