A064212 a(n) = sigma(n) + usigma(n) = A000203(n) + A034448(n).

2, 6, 8, 12, 12, 24, 16, 24, 23, 36, 24, 48, 28, 48, 48, 48, 36, 69, 40, 72, 64, 72, 48, 96, 57, 84, 68, 96, 60, 144, 64, 96, 96, 108, 96, 141, 76, 120, 112, 144, 84, 192, 88, 144, 138, 144, 96, 192, 107, 171, 144, 168, 108, 204, 144, 192, 160

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

Sum_{k=1..n} a(k) ~ (Pi^2/12)*(1 + 1/zeta(3)) * n^2. - Amiram Eldar, Apr 01 2024

Mathematica

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 *)

Prog

(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) }
{ for (n=1, 1000, write("b064212.txt", n, " ", sigma(n) + usigma(n)) ) } \\ Harry J. Smith, Sep 10 2009

Crossrefs

Cf. A000203, A034448, A048146.

Cf. A002117, A072691.

Sequence in context: A054067 A250190 A244342 * A056906 A257056 A209249

Adjacent sequences: A064209 A064210 A064211 * A064213 A064214 A064215

Keyword

nonn

Author

N. J. A. Sloane, Oct 31 2001

Status

approved