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

Author

Marc LeBrun

Keywords

• nonn
• easy
• mult

Links

• N. J. A. Sloane, Transforms.

Crossrefs

Cf. A000045, A000720, A003965.

Programs

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 *)

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

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

Extensions

More terms from David W. Wilson, Aug 29 2001