|
|
A167334
|
|
Totally multiplicative sequence with a(p) = 2*(2p+1) = 4p+2 for prime p.
|
|
1
|
|
|
1, 10, 14, 100, 22, 140, 30, 1000, 196, 220, 46, 1400, 54, 300, 308, 10000, 70, 1960, 78, 2200, 420, 460, 94, 14000, 484, 540, 2744, 3000, 118, 3080, 126, 100000, 644, 700, 660, 19600, 150, 780, 756, 22000, 166, 4200, 174, 4600, 4312, 940, 190, 140000, 900
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
Multiplicative with a(p^e) = (2*(2p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(2*p(k)+1))^e(k).
|
|
MATHEMATICA
|
a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((2*fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 06 2016 *)
f[p_, e_] := (4*p+2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|