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A167314 Totally multiplicative sequence with a(p) = 4*(p-3) for prime p. 1
1, -4, 0, 16, 8, 0, 16, -64, 0, -32, 32, 0, 40, -64, 0, 256, 56, 0, 64, 128, 0, -128, 80, 0, 64, -160, 0, 256, 104, 0, 112, -1024, 0, -224, 128, 0, 136, -256, 0, -512, 152, 0, 160, 512, 0, -320, 176, 0, 256, -256 (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) = (4*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)-3))^e(k). a(3k) = 0 for k >= 1. a(n) = A165825(n) * A166589(n) = 4^bigomega(n) * A166589(n) = 4^A001222(n) * A166589(n).

MATHEMATICA

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*4^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)

CROSSREFS

Sequence in context: A086262 A167361 A321610 * A208451 A207541 A158802

Adjacent sequences:  A167311 A167312 A167313 * A167315 A167316 A167317

KEYWORD

sign,mult

AUTHOR

Jaroslav Krizek, Nov 01 2009

STATUS

approved

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Last modified September 26 06:16 EDT 2021. Contains 347664 sequences. (Running on oeis4.)