OFFSET
1,1
COMMENTS
a(n) > 1 and a(n) = n if n prime. All terms are squarefree.
EXAMPLE
a(6) = 70 = 2*5*7; 2^6 + 5^6 + 7^6 = 133338 = 22223*6.
a(18)= 2*5*7*11*13*17*19*23*29 = 2156564410 because:
p^18 == 10, 9 (mod 18) for p = 2,3 respectively, and p^18 == 1 (mod 18) for p prime > 3. The minimum sum divisible by 18 is s = 2^18 + Sum_{k=3..10} prime(k)^18 whose residues sum to 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 18. Hence a(18) = 2156564410.
MAPLE
with(numtheory): T:=array(1..50):for n from 1 to 50 do:q:=0:for k from 2 to 7000 while(q=0)do:x:=factorset(k):s:=sum(x[j]^n , j=1..nops(x)) :if irem(s, n)=0 then printf ( "%d %d \n", n, k):q:=1:else fi:od:if q=0 then for i from 1 to n do: T[i]:=irem(ithprime(i)^n, n):od:W:=convert(T, set):n1:=nops(W):n2:=W[n1]:n3:=W[n1-1]:
s:=0:p:=1:for a from 1 to n while(s<>n) do: if T[a]= 1 or T[a]=n2 or (T[a] = n3 and n2+n3<n) then s:=s+T[a]:p:=p*ithprime(a):else fi:if s= n then printf ( "%d %d \n", n, p):
else fi:od:else fi:od:
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 08 2011
STATUS
approved