cp's OEIS Frontend

A335073 a(n) = Sum_{k=1..n} 2^(bigomega(k) - omega(k)).

%I A335073 #14 Aug 14 2020 16:46:51
%S A335073 1,2,3,5,6,7,8,12,14,15,16,18,19,20,21,29,30,32,33,35,36,37,38,42,44,
%T A335073 45,49,51,52,53,54,70,71,72,73,77,78,79,80,84,85,86,87,89,91,92,93,
%U A335073 101,103,105,106,108,109,113,114,118,119,120,121,123,124,125,127
%N A335073 a(n) = Sum_{k=1..n} 2^(bigomega(k) - omega(k)).
%C A335073 Partial sums of A162510.
%H A335073 Harvey P. Dale, <a href="/A335073/b335073.txt">Table of n, a(n) for n = 1..1000</a>
%F A335073 a(n) = Sum_{k=1..n} A008683(k) * A069205(floor(n/k)).
%F A335073 a(n) = Sum_{k=1..n} A061142(k) * A002321(floor(n/k)).
%p A335073 a:= proc(n) option remember; uses numtheory; `if`(n<1, 0,
%p A335073       2^(bigomega(n)-nops(factorset(n)))+a(n-1))
%p A335073     end:
%p A335073 seq(a(n), n=1..70);  # _Alois P. Heinz_, May 22 2020
%t A335073 Accumulate[Table[2^(PrimeOmega[n]-PrimeNu[n]),{n,70}]] (* _Harvey P. Dale_, Aug 14 2020 *)
%o A335073 (PARI) a(n) = sum(k=1, n, 2^(bigomega(k) - omega(k)));
%Y A335073 Cf. A001221, A001222, A046660, A061142, A069205, A162510.
%K A335073 nonn
%O A335073 1,2
%A A335073 _Daniel Suteu_, May 22 2020