A167351 Totally multiplicative sequence with a(p) = (p+1)*(p+2) = p^2+3p+2 for prime p.

1, 12, 20, 144, 42, 240, 72, 1728, 400, 504, 156, 2880, 210, 864, 840, 20736, 342, 4800, 420, 6048, 1440, 1872, 600, 34560, 1764, 2520, 8000, 10368, 930, 10080, 1056, 248832, 3120, 4104, 3024, 57600, 1482, 5040, 4200, 72576, 1806, 17280, 1980, 22464

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = ((p+1)*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)+2))^e(k). a(n) = A003959(n) * A166590(n).

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 3*p + 1)) = 1.224476389903759550811745481197762941643093896189832037452375111814242433... - Vaclav Kotesovec, Sep 20 2020

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)

Crossrefs

Sequence in context: A025104 A163323 A060159 * A231400 A231467 A078600

Adjacent sequences: A167348 A167349 A167350 * A167352 A167353 A167354

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved