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A113498
Ascending descending base exponent transform of omega(n) (A001221).
5
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
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
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