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

Author

Jonathan Vos Post, Jan 10 2006

Keywords

• easy
• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

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)).

Extensions

Corrected and extended by Giovanni Resta, Jun 13 2016

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