A349389 a(n) = A349387(n) + A349388(n).

2, 0, 0, 1, 0, 4, 0, 5, 4, 4, 0, 10, 0, 8, 8, 19, 0, 16, 0, 10, 16, 4, 0, 26, 4, 8, 32, 20, 0, 0, 0, 65, 8, 4, 16, 42, 0, 8, 16, 26, 0, 0, 0, 10, 32, 12, 0, 70, 16, 24, 8, 20, 0, 68, 8, 52, 16, 4, 0, 4, 0, 12, 64, 211, 16, 0, 0, 10, 24, 0, 0, 114, 0, 8, 48, 20, 16, 0, 0, 70, 196, 4, 0, 8, 8, 8, 8, 26, 0, 8, 32, 30

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences computed from indices in prime factorization

Formula

a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1<d<n} A349387(d) * A349388(n/d). [As the sequences are Dirichlet inverses of each other]

Mathematica

f1[p_, e_] := (q = NextPrime[p])^e - p * q^(e-1); f2[p_, e_] := p^e - NextPrime[p] * p^(e-1); a[1] = 2; a[n_] := Times @@ f1 @@@ (f = FactorInteger[n]) + Times @@ f2 @@@ f; Array[a, 100] (* Amiram Eldar, Nov 18 2021 *)

Prog

(PARI) A349389(n) = (A349387(n) + A349388(n)); \\ Needs also code from A349387 and A349388.

Crossrefs

Cf. A349387, A349388.

Cf. also A349383.

Sequence in context: A349349 A349443 A319340 * A354876 A323408 A347099

Adjacent sequences: A349386 A349387 A349388 * A349390 A349391 A349392

Keyword

nonn

Author

Antti Karttunen, Nov 17 2021

Status

approved