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A291208 Number of noncube divisors of n. 2
0, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 5, 1, 3, 3, 3, 1, 5, 1, 5, 3, 3, 1, 6, 2, 3, 2, 5, 1, 7, 1, 4, 3, 3, 3, 8, 1, 3, 3, 6, 1, 7, 1, 5, 5, 3, 1, 8, 2, 5, 3, 5, 1, 6, 3, 6, 3, 3, 1, 11, 1, 3, 5, 4, 3, 7, 1, 5, 3, 7, 1, 10, 1, 3, 5, 5, 3, 7, 1, 8, 3, 3, 1, 11, 3, 3, 3, 6, 1, 11, 3, 5, 3, 3, 3, 10, 1, 5, 5, 8, 1, 7, 1, 6, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from exponents in factorization of n

FORMULA

G.f.: Sum_{k>=1} x^A007412(k)/(1 - x^A007412(k)).

G.f.: Sum_{k>=1} (x^k - x^(k^3))/((1 - x^k)*(1 - x^(k^3))).

a(n) = A000005(n) - A061704(n).

EXAMPLE

a(8) = 2 because 8 has 4 divisors {1, 2, 4, 8} among which 2 are noncubes {2, 4}.

MATHEMATICA

nmax = 105; Rest[CoefficientList[Series[Sum[(x^k - x^k^3)/((1 - x^k) (1 - x^k^3)), {k, 1, nmax}], {x, 0, nmax}], x]]

PROG

(PARI) a(n) = sumdiv(n, d, !ispower(d, 3)); \\ Michel Marcus, Aug 21 2017

CROSSREFS

Cf. A000005, A007412, A056595, A061704.

Sequence in context: A323014 A182850 A293227 * A241165 A233183 A035942

Adjacent sequences:  A291205 A291206 A291207 * A291209 A291210 A291211

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 21 2017

STATUS

approved

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Last modified January 25 01:33 EST 2020. Contains 331229 sequences. (Running on oeis4.)