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A167322
Totally multiplicative sequence with a(p) = 3*(p+3) for prime p.
1
1, 15, 18, 225, 24, 270, 30, 3375, 324, 360, 42, 4050, 48, 450, 432, 50625, 60, 4860, 66, 5400, 540, 630, 78, 60750, 576, 720, 5832, 6750, 96, 6480, 102, 759375, 756, 900, 720, 72900, 120, 990, 864, 81000, 132, 8100, 138, 9450, 7776, 1170, 150, 911250, 900
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (3*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)+3))^e(k).
a(n) = A165824(n) * A166591(n) = 3^bigomega(n) * A166591(n) = 3^A001222(n) * A166591(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*3^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (3*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 22 2023 *)
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved