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A167339
Totally multiplicative sequence with a(p) = p*(p-2) = p^2-2p for prime p.
1
1, 0, 3, 0, 15, 0, 35, 0, 9, 0, 99, 0, 143, 0, 45, 0, 255, 0, 323, 0, 105, 0, 483, 0, 225, 0, 27, 0, 783, 0, 899, 0, 297, 0, 525, 0, 1295, 0, 429, 0, 1599, 0, 1763, 0, 135, 0, 2115, 0, 1225, 0
OFFSET
1,3
LINKS
FORMULA
Multiplicative with a(p^e) = (p*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)-2))^e(k).
a(2k) = 0 for k >= 1.
a(n) = n * A166586(n).
Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 1/p^2 + 2/p^3) = 0.1016391193... . - Amiram Eldar, Dec 15 2022
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*n, {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)
CROSSREFS
Cf. A166586.
Sequence in context: A275831 A065121 A334824 * A277936 A138540 A123023
KEYWORD
nonn,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved