A364947 Prime powers that are equal to the sum of the first k prime powers (including 1) for some k.

1, 3, 79, 163, 499, 947, 1279, 5297, 6689, 9629, 10853, 17467, 21001, 23887, 25411, 29761, 32089, 33289, 47947, 49429, 55633, 80687, 84697, 96157, 116719, 119159, 126641, 131783, 136991, 153371, 156227, 167861, 182969, 215249, 243161, 257921, 280897, 288853

Offset: 1

Author

Ilya Gutkovskiy, Aug 14 2023

Keywords

• nonn

Examples

			79 is a term because 79 is a prime power and 79 = 1 + 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11 + 13 + 16 = 1 + 2 + 3 + 2^2 + 5 + 7 + 2^3 + 3^2 + 11 + 13 + 2^4.
		

Links

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

Crossrefs

Intersection of A000961 and A024918.

Cf. A013918, A013921, A013932, A364797

Programs

Mathematica

Select[Accumulate[Select[Range[2000], # == 1 || PrimePowerQ[#] &]], # == 1 || PrimePowerQ[#] &]

PARI

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