A086419 Sum of all prime factors of 3-smooth numbers.

0, 2, 3, 4, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 21, 22, 22, 22, 23, 23, 23, 24, 23, 24, 24, 24, 25, 24, 25, 25, 26, 25, 26, 26, 26, 27

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A001414(A003586(n)).

a(n) = 2*A022328(n) + 3*A022329(n).

Mathematica

s = {}; m = 12; Do[n = 3^k; While[n <= 3^m, AppendTo[s, n]; n*=2], {k, 0, m}]; sopfr[1] = 0; sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; sopfr /@ Union[s] (* Amiram Eldar, Jan 29 2020 *)

Crossrefs

Cf. A001414, A003586, A022328, A022329, A086418, A086417, A069352.

Sequence in context: A195879 A305398 A216522 * A287354 A025548 A121604

Adjacent sequences: A086416 A086417 A086418 * A086420 A086421 A086422

Keyword

nonn

Author

Reinhard Zumkeller, Jul 18 2003

Status

approved