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

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, 45, 49, 51, 52, 53, 54, 70, 71, 72, 73, 77, 78, 79, 80, 84, 85, 86, 87, 89, 91, 92, 93, 101, 103, 105, 106, 108, 109, 113, 114, 118, 119, 120, 121, 123, 124, 125, 127

Offset: 1

Author

Daniel Suteu, May 22 2020

Keywords

• nonn

Comments

Partial sums of A162510.

Links

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

Crossrefs

Cf. A001221, A001222, A046660, A061142, A069205, A162510.

Programs

Maple

a:= proc(n) option remember; uses numtheory; `if`(n<1, 0,
      2^(bigomega(n)-nops(factorset(n)))+a(n-1))
    end:
seq(a(n), n=1..70);  # Alois P. Heinz, May 22 2020

Mathematica

Accumulate[Table[2^(PrimeOmega[n]-PrimeNu[n]),{n,70}]] (* Harvey P. Dale, Aug 14 2020 *)

PARI

a(n) = sum(k=1, n, 2^(bigomega(k) - omega(k)));

Formula

a(n) = Sum_{k=1..n} A008683(k) * A069205(floor(n/k)).

a(n) = Sum_{k=1..n} A061142(k) * A002321(floor(n/k)).