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Numbers of the form 2^k+3^k+...p_n^k.
0

%I #4 Mar 31 2012 13:21:55

%S 2,4,5,8,10,13,16,17,28,32,35,38,41,58,64,77,87,97,100,128,129,160,

%T 197,208,238,256,275,281,328,377,381,440,501,503,512,568,639,666,712,

%U 722,791,793,874,963,1024,1027,1060,1161,1264

%N Numbers of the form 2^k+3^k+...p_n^k.

%C It is conjectured that 160 is the only number to appear twice: 2+3+...+31=160 2^3+3^3+5^3=160

%e 2^2+3^2=4+9=13 2+3+5=10 2^7=128 so these numbers are all present.

%o (PARI) v=vector(1000); vc=1; for (n=1,100,p=primes(n); for (k=1,10, s=0; for (c=1,n,s=s+p[c]^k); v[vc]=s; vc++; )); vecextract(vecsort(v),"1..100")

%K nonn

%O 1,1

%A _Jon Perry_, Nov 10 2002