

A117003


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


5



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
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OFFSET

1,2


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


FORMULA

a(n) = Sum_{dn} max(d, n/d).  Seiichi Manyama, Dec 27 2017
a(n) = Sum_{k in Z} H(4*nk^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


PROG

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


CROSSREFS

Cf. A000203, A079667, A117003, A117004, A259825.
Sequence in context: A129854 A088682 A102415 * A335032 A057670 A171615
Adjacent sequences: A117000 A117001 A117002 * A117004 A117005 A117006


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Apr 15 2006


STATUS

approved



