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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 (list; graph; refs; listen; history; text; internal format)
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).

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

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Last modified February 29 05:01 EST 2020. Contains 332353 sequences. (Running on oeis4.)