A167334 Totally multiplicative sequence with a(p) = 2*(2p+1) = 4p+2 for prime p.

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

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) * A166660(n) = 2^bigomega(n) * A166660(n) = 2^A001222(n) * A166660(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 19 2023 *)

Crossrefs

Cf. A001222, A061142, A166660.

Sequence in context: A258287 A254003 A219682 * A236145 A246769 A322566

Adjacent sequences: A167331 A167332 A167333 * A167335 A167336 A167337

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved