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

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.

Mathematica

Accumulate[Table[If[PrimePowerQ[n], n, 0], {n, 60}]] (* Harvey P. Dale, Oct 04 2019 *)

Prog

(PARI) a(n)=sum(k=1, n, k*if(omega(k)-1, 0, 1))

Crossrefs

Cf. A034387, A081738, A000196.

Sequence in context: A364248 A284916 A070986 * A161767 A235333 A060139

Adjacent sequences: A074790 A074791 A074792 * A074794 A074795 A074796

Keyword

nonn,changed

Author

Benoit Cloitre, Sep 07 2002

Status

approved