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 A167352 Totally multiplicative sequence with a(p) = (p+1)*(p-3) = p^2-2p-3 for prime p. 1
 1, -3, 0, 9, 12, 0, 32, -27, 0, -36, 96, 0, 140, -96, 0, 81, 252, 0, 320, 108, 0, -288, 480, 0, 144, -420, 0, 288, 780, 0, 896, -243, 0, -756, 384, 0, 1292, -960, 0, -324, 1596, 0, 1760, 864, 0, -1440, 2112, 0, 1024, -432, 0, 1260, 2700, 0, 1152, -864, 0 (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+1)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A003959(n) * A166589(n). Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 1/p^2 + 5/p^3 + 3/p^4) = 0.0629795941629... . - Amiram Eldar, Dec 15 2022 MATHEMATICA a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *) CROSSREFS Cf. A003959, A166589. Sequence in context: A248885 A118534 A187427 * A318303 A336710 A294106 Adjacent sequences: A167349 A167350 A167351 * A167353 A167354 A167355 KEYWORD sign,mult AUTHOR Jaroslav Krizek, Nov 01 2009 STATUS approved

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Last modified August 7 12:22 EDT 2024. Contains 375012 sequences. (Running on oeis4.)