

A084738


Smallest prime of the form (n^k1)/(n1), or 0 if no such prime exists.


8



3, 13, 5, 31, 7, 2801, 73, 0, 11, 50544702849929377, 13, 30941, 211, 241, 17, 307, 19, 109912203092239643840221, 421, 463, 23, 292561, 601, 0, 321272407, 757, 29, 732541, 31, 917087137, 0, 1123, 2458736461986831391
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OFFSET

2,1


COMMENTS

As mentioned by Dubner, when n is a power (greater than 1) of a prime, then (n^k1)/(n1) will usually be composite for all k, which is the case for n = 9, 25, 32 and 49.  T. D. Noe, Jan 23 2004
Here, a(n) is the smallest prime of the form (n^k1)/(n1) with k >= 2 while in A285642 it is the smallest prime with k > 2. Differences occur when (n^21)/(n1) = n+1 is prime, and therefore, when n = prime(m)  1 is in A006093 (see formula).  Bernard Schott, Mar 16 2023


LINKS



FORMULA



EXAMPLE

a(8) = 73 = (8^31)/(81).


MATHEMATICA

Table[SelectFirst[(n^#  1)/(n  1) & /@ Range[10^3], PrimeQ] /. k_ /; MissingQ@ k > 0, {n, 2, 34}] (* Michael De Vlieger, Apr 24 2017, Version 10.2 *)


CROSSREFS

Cf. A084740 (least k such that (n^k1)/(n1) is prime).


KEYWORD

nonn


AUTHOR

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003


EXTENSIONS



STATUS

approved



