A277075 Numbers n for which A276711(n) = 1.

2, 4, 5, 8, 9, 10, 16, 22, 24, 25, 26, 36, 58, 64, 76, 82, 85, 120, 170, 196, 202, 214, 324, 328, 370, 412, 505, 562, 676, 706, 730, 799, 841, 1024, 1204, 1243, 1549, 1681, 1849, 2146, 2986, 10404, 46656, 52900, 112896, 122500

Offset: 1

Author

Robert Israel, Sep 27 2016

Keywords

• nonn
• more

Comments

Is the sequence finite?

a(47) > 10^7 if it exists.

Examples

			122500 is in the sequence because 122500 = 121169 + 11^3 is the only way to write 122500 as the sum of a prime and a nonnegative perfect power.
		

Crossrefs

Cf. A276711.

Programs

Maple

N:= 10^6: # to get all terms <= N
Primes:= select(isprime, [2,seq(i,i=3..N,2)]):
Pows:= {0,1,seq(seq(b^k,k=2..floor(log[b](N))),b=2..floor(sqrt(N)))}:
G:= expand(add(x^p,p=Primes)*add(x^r,r=Pows)):
B:= [seq(coeff(G,x,i),i=1..N)]:
select(t -> B[t]=1, [$1..N]);