A076614 Numbers of the form 2^k+3^k+...p_n^k.

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

Links

Table of n, a(n) for n=1..49.

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

Adjacent sequences: A076611 A076612 A076613 * A076615 A076616 A076617

Keyword

nonn

Author

Jon Perry, Nov 10 2002

Status

approved