login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A143348 a(n) = -(-1)^n times sum of divisors of n. 3
1, -3, 4, -7, 6, -12, 8, -15, 13, -18, 12, -28, 14, -24, 24, -31, 18, -39, 20, -42, 32, -36, 24, -60, 31, -42, 40, -56, 30, -72, 32, -63, 48, -54, 48, -91, 38, -60, 56, -90, 42, -96, 44, -84, 78, -72, 48, -124, 57, -93, 72, -98, 54, -120, 72, -120, 80, -90, 60, -168, 62, -96, 104, -127, 84, -144, 68, -126, 96 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..10000

László Tóth, Alternating sums concerning multiplicative arithmetic functions, arXiv preprint arXiv:1608.00795 [math.NT], 2016.

FORMULA

a(n) is multiplicative with a(2^e) = 1 - 2^(e+1) if e > 0, a(p^e) = (p^(e+1) - 1) / (p - 1) if p > 2.

G.f.: Sum_{k>0} k * -(-x)^k / (1 - (-x)^k) = Sum_{k>0} -(-x)^k / (1 - (-x)^k)^2.

Dirichlet g.f.: zeta(s) * zeta(s-1) * (1 - 6 / 2^s + 4 / 4^s).

EXAMPLE

q - 3*q^2 + 4*q^3 - 7*q^4 + 6*q^5 - 12*q^6 + 8*q^7 - 15*q^8 + 13*q^9 + ...

MATHEMATICA

Table[-(-1)^n*DivisorSigma[1, n], {n, 69}] (* Michael De Vlieger, Aug 19 2017 *)

PROG

(PARI) {a(n) = if( n<1, 0, -(-1)^n * sigma(n))}

CROSSREFS

-(-1)^n * A000203(n) = a(n). A143337(n) = 24 * a(n) unless n=0.

Sequence in context: A097863 A287926 A097012 * A000203 A324545 A003979

Adjacent sequences:  A143345 A143346 A143347 * A143349 A143350 A143351

KEYWORD

sign,mult

AUTHOR

Michael Somos, Aug 09 2008

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 November 28 07:44 EST 2020. Contains 338702 sequences. (Running on oeis4.)