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A233541
a(n) = sigma(n) + phi(n) + d(n).
3
3, 6, 8, 12, 12, 18, 16, 23, 22, 26, 24, 38, 28, 34, 36, 44, 36, 51, 40, 56, 48, 50, 48, 76, 54, 58, 62, 74, 60, 88, 64, 85, 72, 74, 76, 112, 76, 82, 84, 114, 84, 116, 88, 110, 108, 98, 96, 150, 102, 119, 108, 128, 108, 146, 116, 152, 120, 122, 120, 196, 124
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
FORMULA
a(n) = A000203(n) + A000010(n) + A000005(n).
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.
MAPLE
with(numtheory); A233541:=n->sigma(n) + phi(n) + tau(n); seq(A233541(n), n=1..100);
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