This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A143519 Moebius transform of A010051, the characteristic function of the primes: a(n) = Sum_{d|n} mu(n/d)*A010051(d); A054525 * A010051. 5
 0, 1, 1, -1, 1, -2, 1, 0, -1, -2, 1, 1, 1, -2, -2, 0, 1, 1, 1, 1, -2, -2, 1, 0, -1, -2, 0, 1, 1, 3, 1, 0, -2, -2, -2, 0, 1, -2, -2, 0, 1, 3, 1, 1, 1, -2, 1, 0, -1, 1, -2, 1, 1, 0, -2, 0, -2, -2, 1, -1, 1, -2, 1, 0, -2, 3, 1, 1, -2, 3, 1, 0, 1, -2, 1, 1, -2, 3, 1, 0, 0, -2, 1, -1, -2, -2, -2, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS A010051 = A051731 * A143519 (since A051731 = the inverse Mobius transform). LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA Mobius transform of A010051, the characteristic function of the primes. Row sums of triangle A143518. a(n) = Sum_{d|n} A010051(d)*A008683(n/d). - Antti Karttunen, Jul 19 2017 EXAMPLE a(4) = -1 since row 4 of triangle A043518 = (0, -1, 0, 0). a(4) = -1 = (0, -1, 0, 1) dot (0, 1, 1, 0), where (0, -1, 0, 1) = row 4 of A054525 and A010051 = (0, 1, 1, 0, 1, 0, 1, 0,...). MATHEMATICA Table[Sum[MoebiusMu[n/d] Boole[PrimeQ@ d], {d, Divisors@ n}], {n, 89}] (* Michael De Vlieger, Jul 19 2017 *) PROG (Sage) def A143519(n) :     D = filter(is_prime, divisors(n))     return add(moebius(n/d) for d in D) [A143519(n) for n in (1..89)]   # Peter Luschny, Feb 01 2012 (PARI) A143519(n) = sumdiv(n, d, isprime(d)*moebius(n/d)); \\ (After Luschny's Sage-code) - Antti Karttunen, Jul 19 2017 CROSSREFS Cf. A008683, A010051, A143518, A054525, A137851. Sequence in context: A203827 A194289 A237194 * A029376 A276790 A029359 Adjacent sequences:  A143516 A143517 A143518 * A143520 A143521 A143522 KEYWORD sign AUTHOR Gary W. Adamson, Aug 22 2008 EXTENSIONS More terms from R. J. Mathar, Jan 19 2009 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.