A143268 a(n) = phi(n)*T(n), where phi(n) is Euler's totient function (A000010) and T(n) = n*(n+1)/2 is the n-th triangular number (A000217).

1, 3, 12, 20, 60, 42, 168, 144, 270, 220, 660, 312, 1092, 630, 960, 1088, 2448, 1026, 3420, 1680, 2772, 2530, 6072, 2400, 6500, 4212, 6804, 4872, 12180, 3720, 14880, 8448, 11220, 9520, 15120, 7992, 25308, 13338, 18720, 13120, 34440, 10836, 39732

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Formula

a(n) = sum of n-th row of triangle A143267.

a(n) = n*(n+1)*phi(n)/2. - Emeric Deutsch, Aug 23 2008

Example

a(4) = 20 = phi(4) * T(4) = 2 * 10.
a(4) = 20 = sum of row 4 terms of triangle A143267: (2 + 4 + 6 + 8).

Maple

with(numtheory): seq((1/2)*n*(n+1)*phi(n), n=1..45); # Emeric Deutsch, Aug 23 2008

Prog

(PARI) a(n)=eulerphi(n)*n*(n+1)/2 \\ Charles R Greathouse IV, Mar 05 2013

Crossrefs

Cf. A000010, A143267.

Sequence in context: A063102 A122576 A212760 * A374072 A193558 A256131

Adjacent sequences: A143265 A143266 A143267 * A143269 A143270 A143271

Keyword

nonn

Author

Gary W. Adamson, Aug 03 2008

Extensions

Extended by Emeric Deutsch, Aug 16 2008

Status

approved