A113498 Ascending descending base exponent transform of omega(n) (A001221).

1, 2, 3, 4, 6, 7, 8, 9, 13, 12, 14, 15, 21, 19, 24, 21, 29, 28, 30, 28, 40, 35, 41, 42, 46, 41, 53, 44, 59, 52, 61, 55, 79, 55, 69, 66, 86, 70, 90, 73, 94, 93, 91, 81, 121, 88, 114, 103, 123, 95, 137, 102, 138, 122, 132, 114, 168, 121, 144, 145, 159, 137, 180

Offset

2,2

Links

G. C. Greubel, Table of n, a(n) for n = 2..5000

Formula

a(n) = Sum_{i=1..n} (omega(k))^(omega(n-k+2)).

a(n) = Sum_{i=1..n} A001221(k))^(A001221(n-k+2)).

Example

Since omega(n) = A001221(n) = 0, 1, 1, 1, 1, 2, 1, 1, 1, 2 and we skip the initial zero term, we have:
a(1) = 1^1 = 1.
a(2) = 1^1 + 1^1 = 2.
a(3) = 1^1 + 1^1 + 1^1 = 3.
a(4) = 1^1 + 1^1 + 1^1 + 1^1 = 4.
a(5) = 1^1 + 1^1 + 1^1 + 1^1 + 2^1 = 6.
a(9) = 1^1 + 1^1 + 1^1 + 1^1 + 2^2 + 1^1 + 1^1 + 1^1 + 2^1 = 13.

Mathematica

Table[Sum[PrimeNu[k]^(PrimeNu[n - k + 2]), {k, 2, n}], {n, 2, 50}] (* G. C. Greubel, May 18 2017 *)

Prog

(PARI) for(n=2, 25, print1(sum(k=2, n, omega(k)^(omega(n-k+2))), ", ")) \\ G. C. Greubel, May 18 2017

Crossrefs

Cf. A001221, A113320, A005408, A113122, A113153, A113154, A113336, A113271, A113258, A113257, A113231, A087316, A113208.

Sequence in context: A128170 A018490 A351038 * A036796 A209643 A039123

Adjacent sequences: A113495 A113496 A113497 * A113499 A113500 A113501

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 10 2006

Extensions

Corrected and extended by Giovanni Resta, Jun 13 2016

Formulas corrected by G. C. Greubel, May 18 2017

Status

approved