|
|
A167312
|
|
Totally multiplicative sequence with a(p) = 2*(p-3) for prime p.
|
|
1
|
|
|
1, -2, 0, 4, 4, 0, 8, -8, 0, -8, 16, 0, 20, -16, 0, 16, 28, 0, 32, 16, 0, -32, 40, 0, 16, -40, 0, 32, 52, 0, 56, -32, 0, -56, 32, 0, 68, -64, 0, -32, 76, 0, 80, 64, 0, -80, 88, 0, 64, -32, 0, 80, 100, 0, 64, -64, 0, -104, 112, 0, 116, -112, 0, 64, 80, 0, 128, 112
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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(3k) = 0 for k >= 1.
|
|
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 08 2016 *)
f[p_, e_] := (2*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|