

A166586


Totally multiplicative sequence with a(p) = p  2 for prime p.


19



1, 0, 1, 0, 3, 0, 5, 0, 1, 0, 9, 0, 11, 0, 3, 0, 15, 0, 17, 0, 5, 0, 21, 0, 9, 0, 1, 0, 27, 0, 29, 0, 9, 0, 15, 0, 35, 0, 11, 0, 39, 0, 41, 0, 3, 0, 45, 0, 25, 0, 15, 0, 51, 0, 27, 0, 17, 0, 57, 0, 59, 0, 5, 0, 33, 0, 65, 0, 21, 0, 69, 0, 71, 0, 9, 0
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OFFSET

1,5


LINKS

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


FORMULA

Multiplicative with a(p^e) = (p2)^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)  2)^e(k). a(2k) = 0 for k >= 1.
a(A000244(n)) = 1.  Michel Marcus, Dec 13 2014
Dirichlet g.f.: 1 / Product_{p prime} (1  p^(1  s) + 2p^s). The Dirichlet inverse is multiplicative with b(p) = 2  p, b(p^e) = 0, for e > 1.  Álvar Ibeas, Nov 24 2017


MAPLE

f:= proc(n) local t;
mul((t[1]2)^t[2], t=ifactors(n)[2])
end proc:
map(f, [$1..100]); # Robert Israel, Jun 07 2016


MATHEMATICA

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]]  2)^fi[[All, 2]])); Table[a[n], {n, 1, 50}] (* G. C. Greubel, Jun 06 2016 *)


PROG

(PARI) a(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = 2); factorback(f); \\ Michel Marcus, Dec 13 2014


CROSSREFS

Cf. A000244 (powers of 3).
Sequence in context: A234434 A234020 A276833 * A122274 A003966 A123931
Adjacent sequences: A166583 A166584 A166585 * A166587 A166588 A166589


KEYWORD

nonn,mult


AUTHOR

Jaroslav Krizek, Oct 17 2009


EXTENSIONS

More terms from Alonso del Arte, Dec 10 2014
a(69) and a(75) corrected by G. C. Greubel, Jun 06 2016
Erroneous formula and program removed by G. C. Greubel, Jun 06 2016


STATUS

approved



