A143231 a(n) = A000010(n) * A002088(n).

1, 2, 8, 12, 40, 24, 108, 88, 168, 128, 420, 184, 696, 384, 576, 640, 1536, 612, 2160, 1024, 1680, 1500, 3784, 1440, 4000, 2544, 4140, 2904, 7560, 2224, 9240, 5184, 6880, 5760, 9216, 4752, 15552, 8100, 11376, 7840, 21200, 6504, 24528, 12080, 15072, 14300

Offset: 1

Author

Gary W. Adamson, Jul 31 2008

Keywords

• nonn

Examples

			a(5) = 40 = A000010(5) * A002088(5) = 4 * 10.
a(5) = 40 = sum of row 5 terms of triangle A143230: (4 + 4 + 8 + 8 + 16).
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..2500

Crossrefs

Cf. A000010, A002088, A143230.

Programs

Magma

A143231:= func< n | EulerPhi(n)*(&+[EulerPhi(k): k in [1..n]]) >;
[A143231(n): n in [1..50]]; // G. C. Greubel, Sep 10 2024

Maple

with(numtheory):
a := proc(n) return phi(n)*add(phi(k),k=1..n): end:
seq(a(n),n=1..46); # Nathaniel Johnston, Jun 26 2011

Mathematica

a[n_]:= a[n]= EulerPhi[n]*Sum[EulerPhi[k], {k,n}];
Table[a[n], {n,50}] (* G. C. Greubel, Sep 10 2024 *)

PARI

a(n)=sum(k=1, n, eulerphi(k))*eulerphi(n) \\ Charles R Greathouse IV, Feb 21 2013

SageMath

def A143231(n): return euler_phi(n)*sum(euler_phi(k) for k in range(1,n+1))
[A143231(n) for n in range(1,51)] # G. C. Greubel, Sep 10 2024

Formula

a(n) = A000010(n) * A002088(n).

a(n) = Sum_{k=1..n} A143230(n,k) (row sums of A143230).

Extensions

Terms after a(14) from Nathaniel Johnston, Jun 26 2011