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

1,2

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A003959, A005596, A072691.

Sequence in context: A123102 A274077 A028272 * A326828 A348398 A132140

Adjacent sequences: A003966 A003967 A003968 * A003970 A003971 A003972

Keyword

nonn,mult

Author

Marc LeBrun

Extensions

More terms from David W. Wilson, Aug 29 2001

Status

approved