A166642 Totally multiplicative sequence with a(p) = 2*(p+1) for prime p.

1, 6, 8, 36, 12, 48, 16, 216, 64, 72, 24, 288, 28, 96, 96, 1296, 36, 384, 40, 432, 128, 144, 48, 1728, 144, 168, 512, 576, 60, 576, 64, 7776, 192, 216, 192, 2304, 76, 240, 224, 2592, 84, 768, 88, 864, 768, 288, 96, 10368, 256, 864

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

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

a(n) = A061142(n) * A003959(n) = 2^bigomega(n) * A003959(n) = 2^A001222(n) * A003959(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*2^(PrimeOmega[n]), {n, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (2*(p+1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

Crossrefs

Cf. A001222, A003959, A061142.

Sequence in context: A356742 A303156 A028321 * A077709 A025627 A038262

Adjacent sequences: A166639 A166640 A166641 * A166643 A166644 A166645

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved