A167330 Totally multiplicative sequence with a(p) = 2*(2p-1) = 4p-2 for prime p.

1, 6, 10, 36, 18, 60, 26, 216, 100, 108, 42, 360, 50, 156, 180, 1296, 66, 600, 74, 648, 260, 252, 90, 2160, 324, 300, 1000, 936, 114, 1080, 122, 7776, 420, 396, 468, 3600, 146, 444, 500, 3888, 162, 1560, 170, 1512, 1800, 540, 186, 12960, 676, 1944

Offset

1,2

Links

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

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).

a(n) = A061142(n) * A166651(n) = 2^bigomega(n) * A166651(n) = 2^A001222(n) * A166651(n).

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 18 2023 *)

Prog

(PARI) a(n) = {my(f=factor(n)); for (k=1, #f~, f[k, 1] = 4*f[k, 1]-2; ); factorback(f); } \\ Michel Marcus, Jun 06 2016

Crossrefs

Cf. A001222, A061142, A166651.

Sequence in context: A348842 A361107 A361325 * A025629 A068889 A203485

Adjacent sequences: A167327 A167328 A167329 * A167331 A167332 A167333

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved