A117003 a(n) = sigma(n) + A079667(n).

1, 4, 6, 10, 10, 18, 14, 24, 21, 30, 22, 44, 26, 42, 40, 52, 34, 66, 38, 70, 56, 66, 46, 100, 55, 78, 72, 98, 58, 122, 62, 112, 88, 102, 84, 156, 74, 114, 104, 156, 82, 168, 86, 154, 138, 138, 94, 216, 105, 170, 136, 182, 106, 216, 132, 212, 152, 174, 118, 294, 122, 186, 186

Offset: 1

Author

N. J. A. Sloane, Apr 15 2006

Keywords

• nonn
• easy

References

• 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.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A013661, A079667, A117004, A259825.

Programs

Mathematica

a[n_] := DivisorSum[n, Max[#, n/#] &]; Array[a, 100] (* Amiram Eldar, Jan 12 2025 *)

PARI

{a(n) = sumdiv(n, d, max(d, n/d))} \\ Seiichi Manyama, Dec 27 2017

Formula

a(n) = Sum_{d|n} max(d, n/d). - Seiichi Manyama, Dec 27 2017

a(n) = Sum_{k in Z} H(4*n-k^2) where H() is the Hurwitz class number. - Seiichi Manyama, Jan 06 2018

G.f.: Sum_{n >= 1} x^(n^2)*(n + 2*x^n - n*x^(2*n))/(1 - x^n)^2 = x + 4*x^2 + 6*x^3 + 10*x^4 + 10*x^5 + .... Cf. A117004. - Peter Bala, Jan 19 2021

Sum_{k=1..n} a(k) ~ zeta(2) * n^2. - Amiram Eldar, Jan 12 2025