A167360 Totally multiplicative sequence with a(p) = (p+2)*(p+3) = p^2+5p+6 for prime p.

1, 20, 30, 400, 56, 600, 90, 8000, 900, 1120, 182, 12000, 240, 1800, 1680, 160000, 380, 18000, 462, 22400, 2700, 3640, 650, 240000, 3136, 4800, 27000, 36000, 992, 33600, 1122, 3200000, 5460, 7600, 5040, 360000, 1560, 9240, 7200, 448000, 1892, 54000, 2070

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = ((p+2)*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+2)*(p(k)+3))^e(k). a(n) = A166590(n) * A166591(n).

Sum_{k>=1} 1/a(k) = Product_{primes p} (1 + 1/(p^2 + 5*p + 5)) = 1.1480407951783735490090642594369977652983537687209929674246821640934042061... - Vaclav Kotesovec, Sep 20 2020

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)

Crossrefs

Cf. A166590, A166591.

Sequence in context: A120210 A181639 A166631 * A113760 A053679 A158844

Adjacent sequences: A167357 A167358 A167359 * A167361 A167362 A167363

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved