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A167304
Totally multiplicative sequence with a(p) = 3*(p+2) for prime p.
1
1, 12, 15, 144, 21, 180, 27, 1728, 225, 252, 39, 2160, 45, 324, 315, 20736, 57, 2700, 63, 3024, 405, 468, 75, 25920, 441, 540, 3375, 3888, 93, 3780, 99, 248832, 585, 684, 567, 32400, 117, 756, 675, 36288, 129, 4860, 135, 5616, 4725, 900, 147, 311040, 729, 5292
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (3*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)+2))^e(k).
a(n) = A165824(n) * A166590(n) = 3^bigomega(n) * A166590(n) = 3^A001222(n) * A166590(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*3^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (3*(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