A003968 Möbius transform of A003959.

1, 2, 3, 6, 5, 6, 7, 18, 12, 10, 11, 18, 13, 14, 15, 54, 17, 24, 19, 30, 21, 22, 23, 54, 30, 26, 48, 42, 29, 30, 31, 162, 33, 34, 35, 72, 37, 38, 39, 90, 41, 42, 43, 66, 60, 46, 47, 162, 56, 60, 51, 78, 53, 96, 55, 126, 57, 58, 59, 90, 61, 62, 84, 486, 65, 66, 67, 102, 69

Offset

1,2

Comments

a(n) = n for squarefree n; otherwise, a(n) > n. - Ivan Neretin, May 13 2015

Dirichlet inverse of A062953. - Werner Schulte, Oct 25 2018

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

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

Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1 + 1/(p^3 - p^2 - p)) = A104141/A005596 = 0.8128327996... . - Amiram Eldar, Oct 23 2022

Mathematica

Table[{pp, aa} = Transpose[FactorInteger[n]]; Times @@ (pp*(pp + 1)^(aa - 1)), {n, 70}]  (* Ivan Neretin, May 13 2015 *)

Prog

(PARI) a(n) = {my(f=factor(n)); for (i=1, #f~, p= f[i, 1]; f[i, 1] = p*(p+1)^(f[i, 2]-1); f[i, 2] = 1); factorback(f); } \\ Michel Marcus, Feb 26 2015

Crossrefs

Cf. A003959, A005596, A062953, A104141.

Sequence in context: A335835 A361480 A142151 * A076734 A242314 A242311

Adjacent sequences: A003965 A003966 A003967 * A003969 A003970 A003971

Keyword

nonn,mult

Author

Marc LeBrun

Extensions

More terms from David W. Wilson, Aug 29 2001

Status

approved