A233541 a(n) = sigma(n) + phi(n) + d(n).

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

Author

Wesley Ivan Hurt, Dec 12 2013

Keywords

• nonn
• easy

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).

Examples

			a(6) = 18; sigma(6) + phi(6) + d(6) = 12 + 2 + 4 = 18.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000010, A000203, A064840.

Programs

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}]

PARI

a(n) = sigma(n) + eulerphi(n) + numdiv(n); \\ Michel Marcus, Dec 07 2016

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