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 A349437 Dirichlet convolution of A252463 with A055615 (Dirichlet inverse of n), where A252463 shifts the prime factorization of odd numbers one step towards smaller primes and divides even numbers by two. 4
 1, -1, -1, 0, -2, 2, -2, 0, -2, 4, -4, 0, -2, 4, 2, 0, -4, 4, -2, 0, 2, 8, -4, 0, -6, 4, -4, 0, -6, -4, -2, 0, 4, 8, 4, 0, -6, 4, 2, 0, -4, -4, -2, 0, 4, 8, -4, 0, -10, 12, 4, 0, -6, 8, 8, 0, 2, 12, -6, 0, -2, 4, 4, 0, 4, -8, -6, 0, 4, -8, -4, 0, -2, 12, 6, 0, 8, -4, -6, 0, -8, 8, -4, 0, 8, 4, 6, 0, -6, -8, 4, 0, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Dirichlet convolution of this sequence with Euler phi (A000010) is A348045. LINKS Antti Karttunen, Table of n, a(n) for n = 1..20000 Index entries for sequences computed from indices in prime factorization FORMULA a(n) = Sum_{d|n} A055615(n/d) * A252463(d). MATHEMATICA f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := If[EvenQ[n], n/2, Times @@ f @@@ FactorInteger[n]]; a[n_] := DivisorSum[n, # * MoebiusMu[#] * s[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 18 2021 *) PROG (PARI) A055615(n) = (n*moebius(n)); A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)}; A252463(n) = if(!(n%2), n/2, A064989(n)); A349437(n) = sumdiv(n, d, A055615(n/d)*A252463(d)); CROSSREFS Cf. A055615, A064989, A252463, A349438 (Dirichlet inverse), A349439 (sum with it). Cf. also A000010, A348045. Sequence in context: A109135 A264136 A274850 * A215594 A230291 A338434 Adjacent sequences: A349434 A349435 A349436 * A349438 A349439 A349440 KEYWORD sign AUTHOR Antti Karttunen, Nov 18 2021 STATUS approved

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Last modified July 21 16:10 EDT 2024. Contains 374475 sequences. (Running on oeis4.)