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

Author

Benoit Cloitre, Sep 07 2002

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A034387, A081738, A000196.

Programs

Mathematica

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

PARI

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

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)