VOOZH about

URL: https://oeis.org/A167321

⇱ A167321 - OEIS

login
A167321
Totally multiplicative sequence with a(p) = 2*(p+3) for prime p.
1
1, 10, 12, 100, 16, 120, 20, 1000, 144, 160, 28, 1200, 32, 200, 192, 10000, 40, 1440, 44, 1600, 240, 280, 52, 12000, 256, 320, 1728, 2000, 64, 1920, 68, 100000, 336, 400, 320, 14400, 80, 440, 384, 16000, 88, 2400, 92, 2800, 2304, 520, 100, 120000, 400, 2560
OFFSET
1,2
LINKS
FORMULA
Multiplicative with a(p^e) = (2*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)+3))^e(k).
a(n) = A061142(n) * A166591(n) = 2^bigomega(n) * A166591(n) = 2^A001222(n) * A166591(n).
MATHEMATICA
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (2*(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