A318782 Numbers m such that a^(s-1) + b^(s-1) + c^(s-1) + ... is prime, where a, b, c, ... are the distinct primes dividing m and s is their sum.

2, 4, 6, 8, 12, 16, 18, 24, 32, 36, 48, 54, 64, 72, 96, 105, 108, 128, 144, 162, 192, 216, 256, 288, 315, 324, 384, 432, 483, 486, 512, 525, 576, 648, 735, 768, 864, 945, 972, 1024, 1152, 1296, 1449, 1458, 1536, 1575, 1728, 1944, 2030, 2048, 2121, 2205, 2301, 2304

Offset

1,1

Comments

The corresponding primes are 2, 97, 684331371443, 37608910510519072144329748463290373800530563, ...

Links

Table of n, a(n) for n=1..54.

Example

105 is in the sequence because the prime factors are {3, 5, 7} with the sum 3 + 5 + 7 = 15, and 3^14 + 5^14 + 7^14 = 684331371443 is a prime number.

Maple

with(numtheory):nn:=1500:
for n from 1 to nn do:
  d:=factorset(n):n0:=nops(d):s0:=add(d[i], i=1..n0):
  p:=add(d[i]^(s0-1), i=1..n0):
  if isprime(p)
  then
     printf(`%d, `, n):
     else fi:
    od:

Mathematica

ok[n_] := Block[{p = First /@ FactorInteger[n]}, PrimeQ@ Total[p^(Total[p] - 1)]]; Select[Range[1024], ok] (* Giovanni Resta, Sep 03 2018 *)

Crossrefs

Cf. A008472.

Sequence in context: A067946 A227270 A145853 * A064527 A333978 A007694

Adjacent sequences: A318779 A318780 A318781 * A318783 A318784 A318785

Keyword

nonn

Author

Michel Lagneau, Sep 03 2018

Extensions

More terms from Giovanni Resta, Sep 03 2018

Status

approved