A167335 Totally multiplicative sequence with a(p) = 2*(3p+1) = 6p+2 for prime p.

1, 14, 20, 196, 32, 280, 44, 2744, 400, 448, 68, 3920, 80, 616, 640, 38416, 104, 5600, 116, 6272, 880, 952, 140, 54880, 1024, 1120, 8000, 8624, 176, 8960, 188, 537824, 1360, 1456, 1408, 78400, 224, 1624, 1600, 87808, 248, 12320, 260, 13328, 12800

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (2*(3p+1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(3*p(k)+1))^e(k).

a(n) = A061142(n) * A166661(n) = 2^bigomega(n) * A166661(n) = 2^A001222(n) * A166661(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((3*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_] := (6*p+2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A061142, A166661.

Sequence in context: A368408 A377904 A064974 * A129244 A070719 A030643

Adjacent sequences: A167332 A167333 A167334 * A167336 A167337 A167338

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved