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a(n) = floor( d(n) * log(n) / 2 ), where d() = A000005.
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%I #8 Apr 07 2024 09:09:35

%S 0,0,1,2,1,3,1,4,3,4,2,7,2,5,5,6,2,8,2,8,6,6,3,12,4,6,6,9,3,13,3,10,6,

%T 7,7,16,3,7,7,14,3,14,3,11,11,7,3,19,5,11,7,11,3,15,8,16,8,8,4,24,4,8,

%U 12,14,8,16,4,12,8,16,4,25,4,8,12,12,8,17,4,21,10,8,4,26,8,8,8,17,4,26,9,13

%N a(n) = floor( d(n) * log(n) / 2 ), where d() = A000005.

%D József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter II, p. 41.

%t a[n_] := Floor[DivisorSigma[0, n] * Log[n] / 2]; Array[a, 100] (* _Amiram Eldar_, Apr 07 2024 *)

%o (PARI) a(n) = numdiv(n) * log(n) \ 2; \\ _Amiram Eldar_, Apr 07 2024

%Y Cf. A000005.

%K nonn

%O 1,4

%A _N. J. A. Sloane_, Jan 24 2003

%E Name corrected by _Amiram Eldar_, Apr 07 2024