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A167313 Totally multiplicative sequence with a(p) = 3*(p-3) for prime p. 1
1, -3, 0, 9, 6, 0, 12, -27, 0, -18, 24, 0, 30, -36, 0, 81, 42, 0, 48, 54, 0, -72, 60, 0, 36, -90, 0, 108, 78, 0, 84, -243, 0, -126, 72, 0, 102, -144, 0, -162, 114, 0, 120, 216, 0, -180, 132, 0, 144, -108 (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) = (3*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (3*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165824(n) * A166589(n) = 3^bigomega(n) * A166589(n) = 3^A001222(n) * A166589(n).

MATHEMATICA

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

CROSSREFS

Sequence in context: A002346 A021327 A297053 * A104780 A176109 A291252

Adjacent sequences:  A167310 A167311 A167312 * A167314 A167315 A167316

KEYWORD

sign,mult

AUTHOR

Jaroslav Krizek, Nov 01 2009

STATUS

approved

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Last modified January 18 14:07 EST 2021. Contains 340254 sequences. (Running on oeis4.)