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A167303
Totally multiplicative sequence with a(p) = 2*(p+2) for prime p.
1
1, 8, 10, 64, 14, 80, 18, 512, 100, 112, 26, 640, 30, 144, 140, 4096, 38, 800, 42, 896, 180, 208, 50, 5120, 196, 240, 1000, 1152, 62, 1120, 66, 32768, 260, 304, 252, 6400, 78, 336, 300, 7168, 86, 1440, 90, 1664, 1400, 400, 98, 40960, 324, 1568
OFFSET
1,2
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(n) = A061142(n) * A166590(n) = 2^bigomega(n) * A166590(n) = 2^A001222(n) * A166590(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 07 2016 *)
f[p_, e_] := (2*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved