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A167360
Totally multiplicative sequence with a(p) = (p+2)*(p+3) = p^2+5p+6 for prime p.
1
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
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
Sequence in context: A120210 A181639 A166631 * A113760 A053679 A158844
KEYWORD
nonn,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved