The On-Line Encyclopedia of Integer Sequences (OEIS)

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A275382

Number of odd prime factors (with multiplicity) of generalized Fermat number 11^(2^n) + 1.
(history; published version)

#14 by N. J. A. Sloane at Wed Jul 27 10:23:06 EDT 2016

STATUS

editing

approved

#13 by N. J. A. Sloane at Wed Jul 27 10:23:03 EDT 2016

NAME

Number of odd prime factors (with multiplicity) of generalized Fermat number of the form 11^(2^n) + 1, n >= 0.

STATUS

proposed

editing

#12 by Arkadiusz Wesolowski at Tue Jul 26 16:11:49 EDT 2016

STATUS

editing

proposed

#11 by Arkadiusz Wesolowski at Tue Jul 26 16:09:02 EDT 2016

EXAMPLE

b(n) = (11^(2^n) + 1)/2.

Complete Factorizations

b(0) = 2*3

b(1) = 61

b(2) = 7321

b(3) = 17*6304673

b(4) = 51329*447600088289

b(5) = 193*257*21283620033217629539178799361

b(6) = 316955440822738177*P49

b(7) = 15361*111489577217*574341646346402207998363393*

4018529583345312964042058778793458689*P55

b(8) = 15190529*4696846849*19618834249745000485889*

4393553986026616439660661873903822389581313*

290103547098489711747952055517085778590240759297*P138

#10 by Arkadiusz Wesolowski at Tue Jul 26 16:08:21 EDT 2016

EXAMPLE

b(n) = (11^(2^n) + 1)/2.

Complete Factorizations

b(0) = 2.3

b(1) = 61

b(2) = 7321

b(3) = 17.6304673

b(4) = 51329.447600088289

b(5) = 193.257.21283620033217629539178799361

b(6) = 316955440822738177.P49

b(7) = 15361.111489577217.574341646346402207998363393.

4018529583345312964042058778793458689.P55

b(8) = 15190529.4696846849.19618834249745000485889.

4393553986026616439660661873903822389581313.

290103547098489711747952055517085778590240759297.P138

#9 by Alois P. Heinz at Tue Jul 26 15:01:35 EDT 2016

STATUS

proposed

editing

#8 by Felix Fröhlich at Mon Jul 25 16:50:50 EDT 2016

STATUS

editing

proposed

Discussion

Tue Jul 26

15:01

Alois P. Heinz: multiplication sign: use * rather than X, ·, or ×; from: https://oeis.org/wiki/Style_Sheet#Spelling_and_notation

#7 by Felix Fröhlich at Mon Jul 25 16:49:33 EDT 2016

FORMULA

a(n) = A001222(A199592(n)) - 1 for n > 0. - Felix Fröhlich, Jul 25 2016

PROG

(PARI) a001222(n) = bigomega(n)

a199592(n) = 11^(2^n)+1

a(n) = if(n==0, 1, a001222(a199592(n))-1) \\ Felix Fröhlich, Jul 25 2016

STATUS

proposed

editing

#6 by Arkadiusz Wesolowski at Mon Jul 25 14:14:33 EDT 2016

STATUS

editing

proposed

#5 by Arkadiusz Wesolowski at Mon Jul 25 13:57:52 EDT 2016

NAME

Number of odd prime factors (with multiplicity) of generalized Fermat number of the form 11^(2^n) + 1, n >= 0.