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

Author

Jaroslav Krizek, Oct 18 2009

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A001222, A003959, A061142.

Programs

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 *)

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).