A318530 Numbers that can be written in more than one way as p^2 + q^3 + r^4 with p, q and r primes.

145, 210, 637, 754, 2317, 2530, 2917, 5218, 5437, 5890, 6447, 6997, 7469, 7653, 7738, 8650, 9333, 11818, 12417, 12796, 14770, 15178, 15197, 15295, 15513, 16349, 16501, 17367, 18389, 19709

Offset: 1

Author

Philippe Guglielmetti, Aug 28 2018

Keywords

• nonn

Examples

			a(1) = 145 = 2^2 + 5^3 + 2^4 = 11^2 + 2^3 + 2^4 .
The first term which can be written in three different ways is
17367 = 23^2 + 13^3 + 11^4 = 113^2 + 13^3 + 7^4 = 131^2 + 5^3 + 3^4 .
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subset of A134657.

Programs

Maple

N:= 10^5: # to get terms <= N
P:= select(isprime, [2,seq(i,i=3..floor(sqrt(N)))]):
Psq:= map(`^`,P,2):
P3:= select(`<=`,map(`^`,P,3),N):
P4:= select(`<=`,map(`^`,P,4),N):
V:= Vector(N):
for a in Psq do for b in P3 do for c in P4 do
   s:= a+b+c;
   if s <= N then V[s]:= V[s]+1 fi
od od od:
select(t -> V[t]>=2, [$1..N]); # Robert Israel, Jan 30 2019