cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A355817 Dirichlet inverse of A010055, characteristic function of powers of primes.

Original entry on oeis.org

1, -1, -1, 0, -1, 2, -1, 0, 0, 2, -1, -1, -1, 2, 2, 0, -1, -1, -1, -1, 2, 2, -1, 0, 0, 2, 0, -1, -1, -6, -1, 0, 2, 2, 2, 2, -1, 2, 2, 0, -1, -6, -1, -1, -1, 2, -1, 0, 0, -1, 2, -1, -1, 0, 2, 0, 2, 2, -1, 6, -1, 2, -1, 0, 2, -6, -1, -1, 2, -6, -1, -1, -1, 2, -1, -1, 2, -6, -1, 0, 0, 2, -1, 6, 2, 2, 2, 0, -1, 6, 2
Offset: 1

Views

Author

Antti Karttunen, Jul 19 2022

Keywords

Comments

Question: Are the absolute values of this sequence given by A335452? Compare also to A355939 and A008480.

Crossrefs

Programs

  • Mathematica
    s[n_] := If[PrimeNu[n] < 2, 1, 0]; a[1] = 1; a[n_] := a[n] = -DivisorSum[n, s[n/#]*a[#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Jul 19 2022 *)
  • PARI
    A010055(n) = ((1==n)||isprimepower(n));
    memoA355817 = Map();
    A355817(n) = if(1==n,1,my(v); if(mapisdefined(memoA355817,n,&v), v, v = -sumdiv(n,d,if(dA010055(n/d)*A355817(d),0)); mapput(memoA355817,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA010055(n/d) * a(d).