A355827 a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A302777(n/d) * a(d).

1, -1, -1, 0, -1, 2, -1, 1, 0, 2, -1, -1, -1, 2, 2, -2, -1, -1, -1, -1, 2, 2, -1, -2, 0, 2, 1, -1, -1, -6, -1, 2, 2, 2, 2, 2, -1, 2, 2, -2, -1, -6, -1, -1, -1, 2, -1, 6, 0, -1, 2, -1, -1, -2, 2, -2, 2, 2, -1, 6, -1, 2, -1, 0, 2, -6, -1, -1, 2, -6, -1, 0, -1, 2, -1, -1, 2, -6, -1, 6, -2, 2, -1, 6, 2, 2, 2, -2, -1, 6, 2

Offset

1,6

Comments

Dirichlet inverse of function f(1) = 1, f(n) = A302777(n) for n > 1, which is the characteristic function of the union of {1} and "Fermi-Dirac primes", A050376.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Index entries for sequences computed from exponents in factorization of n

Mathematica

s[n_] := If[n > 1 && Length[(f = FactorInteger[n])] == 1 && (e = f[[;; , 2]]) == 2^IntegerExponent[e, 2], 1, 0]; a[1] = 1; a[n_] := a[n] = -DivisorSum[n, s[n/#] * a[#] &, # < n &]; Array[a, 100] (* Amiram Eldar, Jul 19 2022 *)

Prog

(PARI)
ispow2(n) = (n && !bitand(n, n-1));
A302777(n) = ispow2(isprimepower(n));
memoA355827 = Map();
A355827(n) = if(1==n, 1, my(v); if(mapisdefined(memoA355827, n, &v), v, v = -sumdiv(n, d, if(d<n, A302777(n/d)*A355827(d), 0)); mapput(memoA355827, n, v); (v)));

Crossrefs

Cf. A050376, A302777.

Cf. also A355817.

Sequence in context: A162642 A366246 A361205 * A139146 A340489 A277487

Adjacent sequences: A355824 A355825 A355826 * A355828 A355829 A355830

Keyword

sign

Author

Antti Karttunen, Jul 19 2022

Status

approved