A167336 Totally multiplicative sequence with a(p) = 2*(4p+1) = 8p+2 for prime p.

1, 18, 26, 324, 42, 468, 58, 5832, 676, 756, 90, 8424, 106, 1044, 1092, 104976, 138, 12168, 154, 13608, 1508, 1620, 186, 151632, 1764, 1908, 17576, 18792, 234, 19656, 250, 1889568, 2340, 2484, 2436, 219024, 298, 2772, 2756, 244944, 330, 27144, 346

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) * A166662(n) = 2^bigomega(n) * A166662(n) = 2^A001222(n) * A166662(n).

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 19 2023 *)

Crossrefs

Cf. A001222, A061142, A166662.

Sequence in context: A093018 A284493 A337523 * A328687 A003634 A338383

Adjacent sequences: A167333 A167334 A167335 * A167337 A167338 A167339

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved