A074793 - OEIS

A074793

Sum of prime powers less than or equal to n.

0, 2, 5, 9, 14, 14, 21, 29, 38, 38, 49, 49, 62, 62, 62, 78, 95, 95, 114, 114, 114, 114, 137, 137, 162, 162, 189, 189, 218, 218, 249, 281, 281, 281, 281, 281, 318, 318, 318, 318, 359, 359, 402, 402, 402, 402, 449, 449, 498, 498, 498, 498, 551, 551, 551, 551, 551

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OFFSET

1,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

Is a(n) asymptotic to c*n^2/log(n) with c=0.55...?

From Daniel Suteu, Aug 20 2023: (Start)

a(n) = Sum_{k=1..floor(log_2(n))} Sum_{p prime <= n^(1/k)} p^k.

a(n) = A034387(n) + A081738(A000196(n)) + Sum_{p prime <= n^(1/3)} ((p^(floor(log_p(n))+1) - 1)/(p-1) - p^2 - p - 1). (End)

EXAMPLE

a(10)=38 because 2,3,4,5,7,8,9 are the prime powers less than or equal to 10 and 2+3+4+5+7+8+9 = 38.