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A003968
Möbius transform of A003959.
15
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
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
KEYWORD
nonn,mult
AUTHOR
EXTENSIONS
More terms from David W. Wilson, Aug 29 2001
STATUS
approved