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A076614
Numbers of the form 2^k+3^k+...p_n^k.
0
2, 4, 5, 8, 10, 13, 16, 17, 28, 32, 35, 38, 41, 58, 64, 77, 87, 97, 100, 128, 129, 160, 197, 208, 238, 256, 275, 281, 328, 377, 381, 440, 501, 503, 512, 568, 639, 666, 712, 722, 791, 793, 874, 963, 1024, 1027, 1060, 1161, 1264
OFFSET
1,1
COMMENTS
It is conjectured that 160 is the only number to appear twice: 2+3+...+31=160 2^3+3^3+5^3=160
EXAMPLE
2^2+3^2=4+9=13 2+3+5=10 2^7=128 so these numbers are all present.
PROG
(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")
CROSSREFS
Sequence in context: A304360 A072437 A115793 * A227800 A144876 A337483
KEYWORD
nonn
AUTHOR
Jon Perry, Nov 10 2002
STATUS
approved