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 A318657 Numerators of the sequence whose Dirichlet convolution with itself yields A087003, a(2n) = 0 and a(2n+1) = moebius(2n+1). 3
 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -5, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,81 COMMENTS Because the corresponding denominator sequence A318658 is equal to A046644 on all odd n, and this sequence as well as A087003 is zero on all even n, it means that also the Dirichlet convolution of a(n)/A046644(n) with itself will yield A087003. Because both A046644 and A087003 are multiplicative, this sequence is also. - Antti Karttunen, Sep 01 2018 LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = numerator of f(n), where f(1) = 1, f(n) = (1/2) * (A087003(n) - Sum_{d|n, d>1, d 1. a(2n) = 0, a(2n-1) = A257098(2n-1), thus multiplicative with a(2^e) = 0, a(p^e) = A257098(p^e) for odd primes p.  - Antti Karttunen, Sep 01 2018 PROG (PARI) up_to = 65537; A087003(n) = ((n%2)*moebius(n)); \\ I.e. a(n) = A000035(n)*A008683(n). DirSqrt(v) = {my(n=#v, u=vector(n)); u[1]=1; for(n=2, n, u[n]=(v[n]/v[1] - sumdiv(n, d, if(d>1&&d

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Last modified May 17 14:19 EDT 2022. Contains 353746 sequences. (Running on oeis4.)