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A167298
Totally multiplicative sequence with a(p) = 6*(p-2) for prime p.
1
1, 0, 6, 0, 18, 0, 30, 0, 36, 0, 54, 0, 66, 0, 108, 0, 90, 0, 102, 0, 180, 0, 126, 0, 324, 0, 216, 0, 162, 0, 174, 0, 324, 0, 540, 0, 210, 0, 396, 0, 234, 0, 246, 0, 648, 0, 270, 0, 900, 0, 540, 0, 306, 0, 972, 0, 612, 0, 342, 0, 354, 0, 1080, 0, 1188, 0, 390
OFFSET
1,3
LINKS
FORMULA
Multiplicative with a(p^e) = (6*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)-2))^e(k).
a(2k) = 0 for k >= 1.
a(n) = A165827(n) * A166586(n) = 6^bigomega(n) * A166586(n) = 6^A001222(n) * A166586(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*6^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (6*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 28 2023 *)
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved