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%I #23 Aug 29 2023 09:27:30
%S 0,1,2,3,4,8,9,10,11,15,16,20,21,25,29,30,31,35,36,40,44,48,49,53,54,
%T 58,59,63,64,73,74,75,79,83,87,91,92,96,100,104,105,114,115,119,123,
%U 127,128,132,133,137,141,145,146,150,154,158,162,166,167,176,177,181
%N a(n) = Sum_{k=1..n} omega(k)^2.
%D G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Fifth edition, Oxford University Press, Chap. XXII, p. 357.
%H Ivan Neretin, <a href="/A069811/b069811.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Turán, <a href="https://doi.org/10.1112/jlms/s1-9.4.274">On a theorem of Hardy and Ramanujan</a>, Journal of the London Mathematical Society, Vol. s1-9, No. 4 (1934), pp. 274-276.
%F a(n) = Sum_{k=1..n} A001221(k)^2.
%F a(n) = n*log(log(n))^2 + O(n*log(log(n))) (Turán, 1934).
%F a(n) = Sum_{k>=1} k^2 * A346617(n,k). - _Alois P. Heinz_, Aug 19 2021
%t Accumulate@((PrimeNu@Range@62)^2) (* _Ivan Neretin_, Mar 16 2017 *)
%o (PARI) a(n) = sum(k=1, n, omega(k)^2); \\ _Michel Marcus_, Mar 16 2017
%Y Equals (A074787(n)-1)/4 for n <= 29.
%Y Cf. A001221, A346617.
%K easy,nonn
%O 1,3
%A _Benoit Cloitre_, Apr 30 2002
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