A003980 Möbius transform of A003965.

1, 1, 2, 2, 4, 2, 7, 4, 6, 4, 12, 4, 20, 7, 8, 8, 33, 6, 54, 8, 14, 12, 88, 8, 20, 20, 18, 14, 143, 8, 232, 16, 24, 33, 28, 12, 376, 54, 40, 16, 609, 14, 986, 24, 24, 88, 1596, 16, 56, 20, 66, 40, 2583, 18, 48, 28, 108, 143, 4180, 16, 6764, 232, 42, 32, 80, 24, 10945, 66

Offset

1,3

Links

Table of n, a(n) for n=1..68.

N. J. A. Sloane, Transforms.

Formula

Multiplicative with a(p^e) = (q-1)q^(e-1) were q = Fibonacci(pi(p)+2) = A000045(A000720(p)+2). - David W. Wilson, Sep 01 2001

Sum_{n>=1} 1/a(n) = Product_{k>=3} (1 + Fibonacci(k)/(Fibonacci(k)-1)^2) = 9.955734312016908009501... . - Amiram Eldar, Sep 14 2023

Mathematica

a[n_] := If[n == 1, 1, Product[{p, e} = pe; q = Fibonacci[PrimePi[p] + 2]; (q-1) q^(e-1), {pe, FactorInteger[n]}]];
Array[a, 100] (* Jean-François Alcover, Sep 29 2020 *)

Prog

(PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2], q); prod(i = 1, #p, q = fibonacci(primepi(p[i])+2); (q-1)*q^(e[i]-1)); } \\ Amiram Eldar, Sep 14 2023

Crossrefs

Cf. A000045, A000720, A003965.

Sequence in context: A275870 A321721 A359102 * A286369 A132801 A321199

Adjacent sequences: A003977 A003978 A003979 * A003981 A003982 A003983

Keyword

nonn,easy,mult

Author

Marc LeBrun

Extensions

More terms from David W. Wilson, Aug 29 2001

Status

approved