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A167302
Totally multiplicative sequence with a(p) = 10*(p-2) for prime p.
1
1, 0, 10, 0, 30, 0, 50, 0, 100, 0, 90, 0, 110, 0, 300, 0, 150, 0, 170, 0, 500, 0, 210, 0, 900, 0, 1000, 0, 270, 0, 290, 0, 900, 0, 1500, 0, 350, 0, 1100, 0, 390, 0, 410, 0, 3000, 0, 450, 0, 2500, 0, 1500, 0, 510, 0, 2700, 0, 1700, 0, 570, 0, 590, 0, 5000, 0, 3300
OFFSET
1,3
LINKS
FORMULA
Multiplicative with a(p^e) = (10*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)-2))^e(k).
a(2k) = 0 for k >= 1.
a(n) = A165831(n) * A166586(n) = 10^bigomega(n) * A166586(n) = 10^A001222(n) * A166586(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*10^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (10*(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