A364797 -id:A364797 - cp's OEIS frontend

A364796 Numbers k such that the sum of the first k prime powers (not including 1) is a prime power.

1, 2, 3, 6, 8, 13, 18, 20, 22, 37, 41, 43, 46, 62, 87, 89, 95, 99, 111, 115, 118, 124, 130, 146, 150, 160, 164, 168, 180, 192, 201, 205, 211, 221, 263, 283, 287, 315, 339, 352, 356, 364, 396, 398, 408, 418, 434, 442, 450, 476, 508, 512, 526, 534, 536, 548, 556, 582

Offset: 1

Ilya Gutkovskiy, Aug 08 2023

nonn

			8 is a term because the sum of the first 8 prime powers 2 + 3 + 4 + 5 + 7 + 8 + 9 + 11 = 49 is a prime power.

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

Cf. A013916, A013919, A013930, A246655, A364797.

Position[Accumulate[Select[Range[4000], PrimePowerQ]], _?PrimePowerQ, Heads -> False] // Flatten

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

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

Original entry on oeis.org

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

Ilya Gutkovskiy, Aug 14 2023

nonn

			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.

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

Intersection of A000961 and A024918.

Cf. A013918, A013921, A013932, A364797

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

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

cp's OEIS Frontend

A364796 Numbers k such that the sum of the first k prime powers (not including 1) is a prime power.

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