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A167297
Totally multiplicative sequence with a(p) = 5*(p-2) for prime p.
1
1, 0, 5, 0, 15, 0, 25, 0, 25, 0, 45, 0, 55, 0, 75, 0, 75, 0, 85, 0, 125, 0, 105, 0, 225, 0, 125, 0, 135, 0, 145, 0, 225, 0, 375, 0, 175, 0, 275, 0, 195, 0, 205, 0, 375, 0, 225, 0, 625, 0, 375, 0, 255, 0, 675, 0, 425, 0, 285, 0, 295, 0, 625, 0, 825, 0, 325, 0, 525
OFFSET
1,3
LINKS
FORMULA
Multiplicative with a(p^e) = (5*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)-2))^e(k).
a(2k) = 0 for k >= 1.
a(n) = A165826(n) * A166586(n) = 5^bigomega(n) * A166586(n) = 5^A001222(n) * A166586(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (5*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved