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A003969
Inverse Möbius transform of A003959.
1
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
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
KEYWORD
nonn,mult
AUTHOR
EXTENSIONS
More terms from David W. Wilson, Aug 29 2001
STATUS
approved