OFFSET
1,1
COMMENTS
a(n) is the sum of the divisors of n plus the number of positive integers less than or equal to n and relatively prime to n plus the number of divisors of n.
If n is a prime, then a(n) = A064840(n). If n is a prime or a semiprime, then a(n) = 2(d(n) + n - 1).
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..10000
FORMULA
Dirichlet g.f.: (zeta(s)^3 + zeta(s-1)*zeta(s)^2 + zeta(s-1))/zeta(s). - Ilya Gutkovskiy, Dec 07 2016
EXAMPLE
a(6) = 18; sigma(6) + phi(6) + d(6) = 12 + 2 + 4 = 18.
MATHEMATICA
Table[DivisorSigma[0, n] + DivisorSigma[1, n] + EulerPhi[n], {n, 100}]
PROG
(PARI) a(n) = sigma(n) + eulerphi(n) + numdiv(n); \\ Michel Marcus, Dec 07 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Dec 12 2013
STATUS
approved