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A167294
Totally multiplicative sequence with a(p) = 2*(p-2) for prime p.
1
1, 0, 2, 0, 6, 0, 10, 0, 4, 0, 18, 0, 22, 0, 12, 0, 30, 0, 34, 0, 20, 0, 42, 0, 36, 0, 8, 0, 54, 0, 58, 0, 36, 0, 60, 0, 70, 0, 44, 0, 78, 0, 82, 0, 24, 0, 90, 0, 100, 0, 60, 0, 102, 0, 108, 0, 68, 0, 114, 0, 118, 0, 40, 0, 132, 0, 130, 0, 84, 0, 138, 0, 142, 0
OFFSET
1,3
LINKS
FORMULA
Multiplicative with a(p^e) = (2*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)-2))^e(k).
a(2k) = 0 for k >= 1.
a(n) = A061142(n) * A166586(n) = 2^bigomega(n) * A166586(n) = 2^A001222(n) * A166586(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 06 2016 *)
f[p_, e_] := (2*(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