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A167356 Totally multiplicative sequence with a(p) = (p-2)*(p-3) = p^2-5p+6 for prime p. 1
1, 0, 0, 0, 6, 0, 20, 0, 0, 0, 72, 0, 110, 0, 0, 0, 210, 0, 272, 0, 0, 0, 420, 0, 36, 0, 0, 0, 702, 0, 812, 0, 0, 0, 120, 0, 1190, 0, 0, 0, 1482, 0, 1640, 0, 0, 0, 1980, 0, 400, 0, 0, 0, 2550, 0, 432, 0, 0, 0, 3192, 0, 3422, 0, 0, 0, 660, 0, 4160, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

FORMULA

Multiplicative with a(p^e) = ((p-2)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)-2)*(p(k)-3))^e(k). a(2k) = 0 for k >= 1, a(3k) = 0 for k >= 1. a(n) = A166586(n) * A166589(n).

MATHEMATICA

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)

CROSSREFS

Cf. A166586, A166589.

Sequence in context: A167298 A242838 A304878 * A219540 A292497 A082731

Adjacent sequences:  A167353 A167354 A167355 * A167357 A167358 A167359

KEYWORD

nonn,mult

AUTHOR

Jaroslav Krizek, Nov 01 2009

STATUS

approved

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Last modified May 9 16:32 EDT 2021. Contains 343742 sequences. (Running on oeis4.)