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A167312 Totally multiplicative sequence with a(p) = 2*(p-3) for prime p. 1
1, -2, 0, 4, 4, 0, 8, -8, 0, -8, 16, 0, 20, -16, 0, 16, 28, 0, 32, 16, 0, -32, 40, 0, 16, -40, 0, 32, 52, 0, 56, -32, 0, -56, 32, 0, 68, -64, 0, -32, 76, 0, 80, 64, 0, -80, 88, 0, 64, -32 (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) = (2*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A061142(n) * A166589(n) = 2^bigomega(n) * A166589(n) = 2^A001222(n) * A166589(n).

MATHEMATICA

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)

CROSSREFS

Sequence in context: A081236 A182059 A103328 * A114122 A319934 A219836

Adjacent sequences:  A167309 A167310 A167311 * A167313 A167314 A167315

KEYWORD

sign,mult

AUTHOR

Jaroslav Krizek, Nov 01 2009

STATUS

approved

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Last modified April 5 15:29 EDT 2020. Contains 333245 sequences. (Running on oeis4.)