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A167301
Totally multiplicative sequence with a(p) = 9*(p-2) for prime p.
1
1, 0, 9, 0, 27, 0, 45, 0, 81, 0, 81, 0, 99, 0, 243, 0, 135, 0, 153, 0, 405, 0, 189, 0, 729, 0, 729, 0, 243, 0, 261, 0, 729, 0, 1215, 0, 315, 0, 891, 0, 351, 0, 369, 0, 2187, 0, 405, 0, 2025, 0, 1215, 0, 459, 0, 2187, 0, 1377, 0, 513, 0, 531, 0, 3645, 0, 2673, 0
OFFSET
1,3
LINKS
FORMULA
Multiplicative with a(p^e) = (9*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)-2))^e(k).
a(2k) = 0 for k >= 1.
a(n) = A165830(n) * A166586(n) = 9^bigomega(n) * A166586(n) = 9^A001222(n) * A166586(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*9^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (9*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved