Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Sep 03 2024 14:54:11
%S 2,6,8,12,12,24,16,24,23,36,24,48,28,48,48,48,36,69,40,72,64,72,48,96,
%T 57,84,68,96,60,144,64,96,96,108,96,141,76,120,112,144,84,192,88,144,
%U 138,144,96,192,107,171,144,168,108,204,144,192,160
%N a(n) = sigma(n) + usigma(n) = A000203(n) + A034448(n).
%H Harry J. Smith, <a href="/A064212/b064212.txt">Table of n, a(n) for n = 1..1000</a>
%F Sum_{k=1..n} a(k) ~ (Pi^2/12)*(1 + 1/zeta(3)) * n^2. - _Amiram Eldar_, Apr 01 2024
%t f1[p_, e_] := (p^(e + 1) - 1)/(p - 1); f2[p_, e_] := p^e + 1; a[n_] := Times @@ f1 @@@ (fct = FactorInteger[n]) + Times @@ f2 @@@ fct; a[1] = 2; Array[a, 100] (* _Amiram Eldar_, Apr 01 2024 *)
%o (PARI) usigma(n)= { local(f,s=1); f=factor(n); for(i=1, matsize(f)[1], s*=1 + f[i, 1]^f[i, 2]); return(s) }
%o { for (n=1, 1000, write("b064212.txt", n, " ", sigma(n) + usigma(n)) ) } \\ _Harry J. Smith_, Sep 10 2009
%Y Cf. A000203, A034448, A048146.
%Y Cf. A002117, A072691.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Oct 31 2001