A364797 Prime powers that are equal to the sum of the first k prime powers (not including 1) for some k.

2, 5, 9, 29, 49, 137, 281, 359, 449, 1579, 2029, 2281, 2677, 5519, 12527, 13229, 15451, 17047, 22409, 24389, 25931, 29191, 32687, 42937, 45757, 53239, 56443, 59743, 70201, 81677, 90863, 95087, 101627, 113111, 169343, 200407, 206911, 256049, 302977, 330133, 338707, 356263

Offset: 1

Author

Ilya Gutkovskiy, Aug 08 2023

Keywords

• nonn

Examples

			49 is a term because 49 is a prime power and 49 = 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013918, A013921, A013932, A246655, A364796.

Programs

Mathematica

Select[Accumulate[Select[Range[2250], PrimePowerQ]], PrimePowerQ]

PARI

list(lim) = {my(s = 0); for(p = 1, lim, if(isprimepower(p), s += p; if(isprimepower(s), print1(s, ", "))));} \\ Amiram Eldar, Jun 20 2025