A167332 Totally multiplicative sequence with a(p) = 2*(4p-1) = 8p-2 for prime p.

1, 14, 22, 196, 38, 308, 54, 2744, 484, 532, 86, 4312, 102, 756, 836, 38416, 134, 6776, 150, 7448, 1188, 1204, 182, 60368, 1444, 1428, 10648, 10584, 230, 11704, 246, 537824, 1892, 1876, 2052, 94864, 294, 2100, 2244, 104272, 326, 16632, 342, 16856

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Multiplicative with a(p^e) = (2*(4p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(4*p(k)-1))^e(k).

a(n) = A061142(n) * A166653(n) = 2^bigomega(n) * A166653(n) = 2^A001222(n) * A166653(n).

Maple

f:=n -> mul((8*t[1]-2)^t[2], t=ifactors(n)[2]):
map(f, [$1..100]); # Robert Israel, Jun 06 2016

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((4*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_] := (8*p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

Prog

(PARI) a(n) = {my(f=factor(n)); for (k=1, #f~, f[k, 1] = 8*f[k, 1]-2; ); factorback(f); } \\ Michel Marcus, Jun 06 2016

Crossrefs

Cf. A001222, A061142, A166653.

Sequence in context: A054276 A305729 A344135 * A291160 A133150 A005734

Adjacent sequences: A167329 A167330 A167331 * A167333 A167334 A167335

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved