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Prime powers that are equal to the sum of the first k prime powers (including 1) for some k.
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%I #4 Aug 24 2023 10:33:32

%S 1,3,79,163,499,947,1279,5297,6689,9629,10853,17467,21001,23887,25411,

%T 29761,32089,33289,47947,49429,55633,80687,84697,96157,116719,119159,

%U 126641,131783,136991,153371,156227,167861,182969,215249,243161,257921,280897,288853

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

%e 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.

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

%Y Intersection of A000961 and A024918.

%Y Cf. A013918, A013921, A013932, A364797

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Aug 14 2023