A108315 Composite numbers n such that a^v + b^v + c^v + ... is prime, where a*b*c* ... is the prime factorization of n and v is the number of primes dividing n (counted with repetition).

6, 10, 12, 14, 26, 28, 34, 40, 45, 52, 63, 74, 75, 80, 94, 96, 117, 126, 134, 146, 152, 153, 165, 175, 194, 206, 245, 261, 268, 274, 296, 320, 325, 326, 333, 334, 363, 376, 384, 386, 387, 399, 466, 468, 475, 477, 486, 490, 500, 504, 507, 522, 531, 536, 539, 550

Offset

1,1

Comments

5166592 generates a 41 digit prime. Some consecutive terms are (74,75) (152,153) (325,326) ... Conjecture: there are infinitely many consecutive values.

Links

Table of n, a(n) for n=1..56.

Example

a(5)=26 because 26=2*13 and 2^2 + 13^2 = 173, a prime.

Mathematica

pfnvQ[n_]:=Module[{fi=Flatten[Table[#[[1]], #[[2]]]&/@FactorInteger[n]]}, CompositeQ[n]&&PrimeQ[Total[fi^PrimeOmega[n]]]]; Select[Range[600], pfnvQ] (* Harvey P. Dale, Jul 21 2018 *)

Crossrefs

Cf. A001222, A082813.

Sequence in context: A325231 A134620 A355791 * A134616 A362180 A081390

Adjacent sequences: A108312 A108313 A108314 * A108316 A108317 A108318

Keyword

easy,nonn

Author

Jason Earls, Jun 30 2005

Status

approved