OFFSET
1,2
COMMENTS
All terms are even. a(n)=2 if and only if n is prime. - Robert Israel, Jan 16 2020
LINKS
FORMULA
EXAMPLE
a(4) = 4 because 4^3 = 64 has 7 divisors {1, 2, 4, 8, 16, 32, 64} among which 4 divisors {2, 4, 16, 32} are noncubes.
MAPLE
f:= proc(n) local F;
F:= map(t -> t[2], ifactors(n)[2]);
mul(1+3*t, t=F) - mul(1+t, t=F)
end proc:
map(f, [$1..100]; # Robert Israel, Jan 16 2020
MATHEMATICA
nmax = 85; Rest[CoefficientList[Series[Sum[(3^PrimeNu[k] - 1) x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]]
a[n_] := Length[Select[Divisors[n], ! IntegerQ[#^(1/3)] &]]; Table[a[n^3], {n, 1, 85}]
Table[DivisorSigma[0, n^3] - DivisorSigma[0, n], {n, 1, 85}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 07 2018
STATUS
approved