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A227979
Integers not of the form (a^k+b^k)/(a+b) for any positive integer values of a, b, k with b > a.
2
2, 4, 6, 8, 9, 14, 16, 18, 22, 23, 24, 32, 33, 36, 38, 42, 44, 46, 47, 54, 56, 59, 62, 64, 66, 69, 71, 72, 77, 81, 83, 86, 88, 92, 94, 96, 98, 99, 107, 114, 118, 121, 126, 128, 131, 132, 134, 138, 141, 142, 144, 152, 154, 158, 161, 162, 166, 167, 168, 177
OFFSET
1,1
COMMENTS
This form, (a^k+b^k)/(a+b), is a generalization of the Fermat numbers.
Not all integers are in this set.
See A229791 for the complement of this sequence.
LINKS
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
Eric Weisstein's World of Mathematics, Repunit.
MATHEMATICA
limit=200; lst = {}; Do[p = (a^k + b^k)/(a + b); If[p <= limit && IntegerQ[p], AppendTo[lst, p]], {k, Log[2, 3*limit+1]}, {b, 2, limit*2}, {a, b-1}]; Complement[Range[limit], Union[lst]]
CROSSREFS
A few of the sequences using this form that identify primes are A000978, A007658, A057469, A128066, A057171, A082387, A122853, A128335.
Sequence in context: A125990 A319776 A191921 * A349151 A080223 A156759
KEYWORD
nonn
AUTHOR
Robert Price, Sep 30 2013
STATUS
approved