1,1

I have checked for powers out to the 250000th prime and the last element found is at the 6420th prime, 64067. It is interesting to note that the only powers so far are squares. Finding a higher power would be interesting.

a(n)=sum(prime(j), j=1..N_n) and a(n) is a power.

a(1)=441 since sum(primes<=59)=440 and 441=21^2.

with(numtheory); egcd := proc(n) local L; L:=map(proc(z) z[2] end, ifactors(n)[2]); igcd(op(L)) end: s := proc(n) option remember; local p; if n=1 then [1, 2] else [n, s(n-1)[2]+ithprime(n)] fi end; t := proc(n) option remember; [n, s(n)[2]+1] fi end; PW:=[]; for z to 1 do for j from 1 to 250000 do if egcd(t(j)[2])>1 then PW:=[op(PW), t(j)] fi od od; PW;

Cf. A007504, A110979.

Sequence in context: A057950 A014793 A151656 this_sequence A013769 A013899 A075268

Adjacent sequences: A110993 A110994 A110995 this_sequence A110997 A110998 A110999

nonn

Walter A. Kehowski (wkehowski(AT)cox.net), Sep 30 2005