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%I #17 Feb 17 2019 19:37:11
%S 1,1,2,2,4,2,2,4,6,4,10,4,4,2,8,8,16,6,6,8,4,10,22,8,20,4,18,4,28,8,
%T 10,16,20,16,8,12,12,6,8,16,40,4,14,20,24,22,46,16,14,20,32,8,52,18,
%U 40,8,12,28,58,16,20,10,12,32,16,20,22,32,44,8,70,24,24,12,40,12,20,8,26,32,54
%N a(n) = phi(n)/3^b(n), where b(n) is #{primes p=1 mod 3 dividing n}.
%C Cubic analog of A070306. Always an integer.
%H Alois P. Heinz, <a href="/A115070/b115070.txt">Table of n, a(n) for n = 1..10000</a>
%H S. R. Finch and Pascal Sebah, <a href="https://arxiv.org/abs/math/0604465">Squares and Cubes Modulo n</a> arXiv:math/0604465 [math.NT], 2006-2016 (v3).
%p with(numtheory):
%p a:= n-> phi(n)/3^add(`if`(irem(p, 3)=1, 1, 0), p=factorset(n)):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Feb 17 2019
%t b[n_] := Count[FactorInteger[n][[All, 1]], p_ /; Mod[p, 3] == 1];
%t a[n_] := EulerPhi[n]/3^b[n];
%t Table[a[n], {n, 1, 81}] (* _Jean-François Alcover_, Feb 17 2019 *)
%o (PARI) {b(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i]%3==1)};
%o {a(n)= eulerphi(n)/3^b(n)};
%o vector(80, n, a(n)) \\ _G. C. Greubel_, Feb 17 2019
%Y Cf. A000010, A005088, A070306, A060839.
%K nonn
%O 1,3
%A _Steven Finch_, Mar 01 2006
%E a(1)=1 prepended by _Alois P. Heinz_, Feb 17 2019
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