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

%I A113498 #15 Sep 08 2024 13:50:36
%S A113498 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,
%T A113498 41,53,44,59,52,61,55,79,55,69,66,86,70,90,73,94,93,91,81,121,88,114,
%U A113498 103,123,95,137,102,138,122,132,114,168,121,144,145,159,137,180
%N A113498 Ascending descending base exponent transform of omega(n) (A001221).
%H A113498 G. C. Greubel, <a href="/A113498/b113498.txt">Table of n, a(n) for n = 2..5000</a>
%F A113498 a(n) = Sum_{i=1..n} (omega(k))^(omega(n-k+2)).
%F A113498 a(n) = Sum_{i=1..n} (A001221(k))^(A001221(n-k+2)).
%e A113498 Since omega(n) = A001221(n) = 0, 1, 1, 1, 1, 2, 1, 1, 1, 2 and we skip the initial zero term, we have:
%e A113498 a(1) = 1^1 = 1.
%e A113498 a(2) = 1^1 + 1^1 = 2.
%e A113498 a(3) = 1^1 + 1^1 + 1^1 = 3.
%e A113498 a(4) = 1^1 + 1^1 + 1^1 + 1^1 = 4.
%e A113498 a(5) = 1^1 + 1^1 + 1^1 + 1^1 + 2^1 = 6.
%e A113498 a(9) = 1^1 + 1^1 + 1^1 + 1^1 + 2^2 + 1^1 + 1^1 + 1^1 + 2^1 = 13.
%t A113498 Table[Sum[PrimeNu[k]^(PrimeNu[n - k + 2]), {k, 2, n}], {n, 2, 50}] (* _G. C. Greubel_, May 18 2017 *)
%o A113498 (PARI) for(n=2,25, print1(sum(k=2,n, omega(k)^(omega(n-k+2))), ", ")) \\ _G. C. Greubel_, May 18 2017
%Y A113498 Cf. A001221, A113320, A005408, A113122, A113153, A113154, A113336, A113271, A113258, A113257, A113231, A087316, A113208.
%K A113498 easy,nonn
%O A113498 2,2
%A A113498 _Jonathan Vos Post_, Jan 10 2006
%E A113498 Corrected and extended by _Giovanni Resta_, Jun 13 2016
%E A113498 Formulas corrected by _G. C. Greubel_, May 18 2017