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A167357
Totally multiplicative sequence with a(p) = (p-2)*(p+3) = p^2+p-6 for prime p.
1
1, 0, 6, 0, 24, 0, 50, 0, 36, 0, 126, 0, 176, 0, 144, 0, 300, 0, 374, 0, 300, 0, 546, 0, 576, 0, 216, 0, 864, 0, 986, 0, 756, 0, 1200, 0, 1400, 0, 1056, 0, 1716, 0, 1886, 0, 864, 0, 2250, 0, 2500, 0, 1800, 0, 2856, 0, 3024, 0, 2244, 0, 3534, 0, 3776, 0, 1800
OFFSET
1,3
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(2k) = 0 for k >= 1.
a(n) = A166586(n) * A166591(n).
Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 - 2/p^2 + 5/p^3 + 6/p^4) = 0.1449357432... . - Amiram Eldar, Dec 15 2022
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: A292497 A082731 A272673 * A064381 A062254 A028849
KEYWORD
nonn,mult
AUTHOR
Jaroslav Krizek, Nov 01 2009
STATUS
approved