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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). 0
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 (list; graph; refs; listen; history; text; internal format)
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: A028919 A325231 A134620 * A134616 A081390 A210578

Adjacent sequences:  A108312 A108313 A108314 * A108316 A108317 A108318

KEYWORD

easy,nonn

AUTHOR

Jason Earls, Jun 30 2005

STATUS

approved

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)