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A167361
Totally multiplicative sequence with a(p) = (p-3)^2 = p^2-6p+9 for prime p.
1
1, 1, 0, 1, 4, 0, 16, 1, 0, 4, 64, 0, 100, 16, 0, 1, 196, 0, 256, 4, 0, 64, 400, 0, 16, 100, 0, 16, 676, 0, 784, 1, 0, 196, 64, 0, 1156, 256, 0, 4, 1444, 0, 1600, 64, 0, 400, 1936, 0, 256, 16, 0, 100, 2500, 0, 256, 16, 0, 676, 3136, 0, 3364, 784, 0, 1, 400
OFFSET
1,5
LINKS
FORMULA
Multiplicative with a(p^e) = ((p-3)^2)^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-3)^2)^e(k).
a(3k) = 0 for k >= 1.
a(n) = A166589(n)^2.
Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 5/p^2 - 3/p^3 - 9/p^4) = 0.07909568395... . - Amiram Eldar, Dec 15 2022
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]^2, {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)
CROSSREFS
Cf. A166589.
Sequence in context: A003195 A190759 A086262 * A321610 A167314 A208451
KEYWORD
nonn,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved