A167355 Totally multiplicative sequence with a(p) = (p-2)*(p+2) = p^2-4 for prime p.

1, 0, 5, 0, 21, 0, 45, 0, 25, 0, 117, 0, 165, 0, 105, 0, 285, 0, 357, 0, 225, 0, 525, 0, 441, 0, 125, 0, 837, 0, 957, 0, 585, 0, 945, 0, 1365, 0, 825, 0, 1677, 0, 1845, 0, 525, 0, 2205, 0, 2025, 0, 1425, 0, 2805, 0, 2457, 0, 1785, 0, 3477, 0, 3717, 0, 1125

Offset

1,3

Links

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

Formula

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

a(2k) = 0 for k >= 1.

a(n) = A166586(n) * A166590(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 - 1/p^2 + 4/p^3 + 4/p^4) = 0.128353657048... . - 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]] - 2)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)

Crossrefs

Cf. A166586, A166590.

Sequence in context: A022902 A291926 A056461 * A282577 A279030 A176868

Adjacent sequences: A167352 A167353 A167354 * A167356 A167357 A167358

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved