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 A167355 Totally multiplicative sequence with a(p) = (p-2)*(p+2) = p^2-4 for prime p. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 18 21:47 EDT 2024. Contains 376002 sequences. (Running on oeis4.)