

A167313


Totally multiplicative sequence with a(p) = 3*(p3) 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
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OFFSET

1,2


LINKS

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


FORMULA

Multiplicative with a(p^e) = (3*(p3))^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



