A003969 Inverse Möbius transform of A003959.

1, 4, 5, 13, 7, 20, 9, 40, 21, 28, 13, 65, 15, 36, 35, 121, 19, 84, 21, 91, 45, 52, 25, 200, 43, 60, 85, 117, 31, 140, 33, 364, 65, 76, 63, 273, 39, 84, 75, 280, 43, 180, 45, 169, 147, 100, 49, 605, 73, 172, 95, 195, 55, 340, 91, 360, 105, 124, 61, 455, 63, 132, 189

Offset: 1

Author

Marc LeBrun

Keywords

• nonn
• mult

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003959, A005596, A072691.

Programs

Mathematica

f[p_, e_] := ((p + 1)^(e + 1) - 1)/p; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 23 2022 *)

PARI

a(n) = {my(f = factor(n)); prod(i = 1, #f~, ((f[i,1] + 1)^(f[i,2] + 1) - 1)/f[i,1]); } \\ Amiram Eldar, Oct 23 2022

Formula

Multiplicative with a(p^e) = ((p+1)^(e+1)-1)/p. - David W. Wilson, Sep 01 2001

Sum_{k=1..n} a(k) ~ c * n^2, where c = A072691/A005596 = 2.199369... . - Amiram Eldar, Oct 23 2022

Extensions

More terms from David W. Wilson, Aug 29 2001