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A167316
Totally multiplicative sequence with a(p) = 6*(p-3) for prime p.
1
1, -6, 0, 36, 12, 0, 24, -216, 0, -72, 48, 0, 60, -144, 0, 1296, 84, 0, 96, 432, 0, -288, 120, 0, 144, -360, 0, 864, 156, 0, 168, -7776, 0, -504, 288, 0, 204, -576, 0, -2592, 228, 0, 240, 1728, 0, -720, 264, 0, 576, -864, 0, 2160, 300, 0, 576, -5184, 0, -936, 336
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (6*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)-3))^e(k).
a(3k) = 0 for k >= 1.
a(n) = A165827(n) * A166589(n) = 6^bigomega(n) * A166589(n) = 6^A001222(n) * A166589(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*6^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (6*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 22 2023 *)
CROSSREFS
KEYWORD
sign,easy,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved