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

1,1

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

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

Cf. A000005, A000010, A000203, A064840.

Sequence in context: A352211 A160277 A080598 * A077148 A246456 A070528

Adjacent sequences: A233538 A233539 A233540 * A233542 A233543 A233544

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 12 2013

Status

approved