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A110997 Powers equal to (sum of first n primes) minus 1. 1
4, 9, 16, 27, 128, 196, 839056 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

I have checked out to the first 250000 primes but the last entry is at the 504th prime, 3607.

LINKS

Table of n, a(n) for n=1..7.

FORMULA

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

EXAMPLE

Since sum(prime(j),j=1..10)=129, 128=2^7.

MAPLE

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 p:=ithprime(n); [n, s(n-1)[2]+p] fi end; t := proc(n) option remember; [n, s(n)[2]-1] 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;

MATHEMATICA

s = 0; Do[s = s + Prime[n]; If[GCD @@ Transpose[ FactorInteger[s - 1]][[2]] > 1, Print[s - 1]], {n, 10^6}] (* Robert G. Wilson v, Oct 02 2005 *)

CROSSREFS

Cf. A007504, A110979.

Sequence in context: A283549 A137354 A113495 * A001640 A161328 A073141

Adjacent sequences:  A110994 A110995 A110996 * A110998 A110999 A111000

KEYWORD

nonn

AUTHOR

Walter Kehowski, Sep 30 2005

STATUS

approved

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Last modified June 15 22:06 EDT 2021. Contains 345053 sequences. (Running on oeis4.)