A133725 a(n) = Sum_{d|n} mu(n/d)*d*(3*d - 1)/2.

1, 4, 11, 17, 34, 35, 69, 70, 105, 106, 175, 142, 246, 213, 284, 284, 424, 321, 531, 428, 570, 535, 781, 572, 890, 750, 963, 858, 1246, 860, 1425, 1144, 1430, 1288, 1716, 1290, 2034, 1611, 2004, 1720, 2500, 1722, 2751, 2150, 2580, 2365, 3289, 2296, 3507, 2690

Offset

1,2

Comments

Previous name was: A054525 * A000326.

Links

Table of n, a(n) for n=1..50.

Formula

Möbius transform of the pentagonal numbers.

G.f.: Sum_{k>=1} mu(k) * x^k * (1 + 2*x^k) / (1 - x^k)^3. - Ilya Gutkovskiy, Sep 17 2021

Example

a(4) = 17 = (0, -1, 0, 1) dot (1, 5, 12, 22) = (0, -5, 0, 22).

Maple

read("transforms") : A000326 := proc(n) n*(3*n-1)/2 ; end: a000326 := [seq(A000326(n), n=1..300)] ; a133725 := MOBIUS(a000326) ; for i from 1 to nops(a133725) do printf("%d, ", op(i, a133725)) ; od: # R. J. Mathar, Jan 19 2009

Crossrefs

Cf. A000326, A007434, A007438, A054525.

Sequence in context: A063237 A026381 A063556 * A050395 A368424 A059771

Adjacent sequences: A133722 A133723 A133724 * A133726 A133727 A133728

Keyword

nonn

Author

Gary W. Adamson, Sep 21 2007

Extensions

More terms from R. J. Mathar, Jan 19 2009

New name from Ilya Gutkovskiy, Sep 17 2021

Status

approved