login
a(n) = sigma(n) - A079667(n).
9

%I #20 Jan 01 2020 13:35:54

%S 1,2,2,4,2,6,2,6,5,6,2,12,2,6,8,10,2,12,2,14,8,6,2,20,7,6,8,14,2,22,2,

%T 14,8,6,12,26,2,6,8,24,2,24,2,14,18,6,2,32,9,16,8,14,2,24,12,28,8,6,2,

%U 42,2,6,22,22,12,24,2,14,8,30,2,48,2,6,18,14,16,24,2,40,17,6,2,46,12,6,8,30

%N a(n) = sigma(n) - A079667(n).

%D H. J. S. Smith, Report on the Theory of Numbers, reprinted in Vol. 1 of his Collected Math. Papers, Chelsea, NY, 1979, see p. 322.

%H Seiichi Manyama, <a href="/A117004/b117004.txt">Table of n, a(n) for n = 1..10000</a>

%F G.f.: sum(n>=1, n*x^(n^2)*(1+x^n)/(1-x^n) ). [_Joerg Arndt_, Jan 30 2011]

%F a(n) = Sum_{d|n} min(d, n/d). - _Seiichi Manyama_, Dec 27 2017

%t Table[Total[Min[#,n/#]&/@Divisors[n]],{n,90}] (* _Harvey P. Dale_, Jan 01 2020 *)

%o (PARI) {a(n) = sumdiv(n, d, min(d, n/d))} \\ _Seiichi Manyama_, Dec 27 2017

%Y Cf. A000203, A079667.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Apr 15 2006