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A166589 Totally multiplicative sequence with a(p) = p-3 for prime p. 16
1, -1, 0, 1, 2, 0, 4, -1, 0, -2, 8, 0, 10, -4, 0, 1, 14, 0, 16, 2, 0, -8, 20, 0, 4, -10, 0, 4, 26, 0, 28, -1, 0, -14, 8, 0, 34, -16, 0, -2, 38, 0, 40, 8, 0, -20, 44, 0, 16, -4, 0, 10, 50, 0, 16, -4, 0, -26, 56, 0, 58, -28, 0, 1, 20, 0, 64, 14, 0, -8, 68, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..72.

FORMULA

Multiplicative with a(p^e) = (p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)-3)^e(k). a(3k) = 0 for k >= 1. Abs (a(2^k)) = 1 for k >= 1.

MATHEMATICA

a[1] = 1; a[p_?PrimeQ] := p-3; a[n_] := Times @@ Power @@@ ({#[[1]]-3, #[[2]]}& /@ FactorInteger[n]); Array[a, 72] (* Jean-Fran├žois Alcover, Jul 19 2017 *)

PROG

(PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i, 1] -=3); factorback(f); \\ Michel Marcus, Jun 09 2014

CROSSREFS

Cf. A166586.

Sequence in context: A265158 A210444 A226949 * A255330 A291940 A153345

Adjacent sequences:  A166586 A166587 A166588 * A166590 A166591 A166592

KEYWORD

sign,mult

AUTHOR

Jaroslav Krizek, Oct 17 2009

EXTENSIONS

More terms from Michel Marcus, Jun 09 2014

STATUS

approved

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Last modified October 18 08:51 EDT 2018. Contains 316313 sequences. (Running on oeis4.)