login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A202535 n*phi(n)*abs( mobius(n) ). 2
1, 2, 6, 0, 20, 12, 42, 0, 0, 40, 110, 0, 156, 84, 120, 0, 272, 0, 342, 0, 252, 220, 506, 0, 0, 312, 0, 0, 812, 240, 930, 0, 660, 544, 840, 0, 1332, 684, 936, 0, 1640, 504, 1806, 0, 0, 1012, 2162, 0, 0, 0, 1632, 0, 2756, 0, 2200, 0, 2052, 1624, 3422 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The inverse Mobius transform is b(n>=1) = 1, 3, 7, 3, 21, 21, 43, 3,7, 63, 11, 21,...., multiplicative with b(p^e) = A002061(p), e>=1 (see A119959). - Mathar

a(n) > 0 only when n is squarefree. - Alonso del Arte, Dec 20 2011

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A002618(n) *A008966(n).

Multiplicative with a(p^e) = (p-1)*p if e=1, a(p^e)=0 if e>1.

Dirichlet g.f. sum_(n>=1) a(n)/n^s = product_{primes p} (1-p^(1-s)+p^(2-s)).

EXAMPLE

a(5) = 20 because 5 phi(5) |mu(5)| = 5 * 4 * |(-1)| = 20.

MATHEMATICA

Table[n EulerPhi[n] Abs[MoebiusMu[n]], {n, 60}] (* Alonso del Arte, Dec 20 2011 *)

PROG

(PARI) a(n)=n*eulerphi(n)*abs(moebius(n)) \\ Charles R Greathouse IV, Dec 20 2011

CROSSREFS

Cf. A079579.

Sequence in context: A243015 A139717 A285119 * A138703 A106458 A213323

Adjacent sequences:  A202532 A202533 A202534 * A202536 A202537 A202538

KEYWORD

nonn,mult,easy

AUTHOR

R. J. Mathar, Dec 20 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)