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 A074793 Sum of prime powers less than or equal to n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 26 07:50 EDT 2023. Contains 365654 sequences. (Running on oeis4.)