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A115070
a(n) = phi(n)/3^b(n), where b(n) is #{primes p=1 mod 3 dividing n}.
1
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, 10, 16, 20, 16, 8, 12, 12, 6, 8, 16, 40, 4, 14, 20, 24, 22, 46, 16, 14, 20, 32, 8, 52, 18, 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
OFFSET
1,3
COMMENTS
Cubic analog of A070306. Always an integer.
LINKS
S. R. Finch and Pascal Sebah, Squares and Cubes Modulo n arXiv:math/0604465 [math.NT], 2006-2016 (v3).
MAPLE
with(numtheory):
a:= n-> phi(n)/3^add(`if`(irem(p, 3)=1, 1, 0), p=factorset(n)):
seq(a(n), n=1..100); # Alois P. Heinz, Feb 17 2019
MATHEMATICA
b[n_] := Count[FactorInteger[n][[All, 1]], p_ /; Mod[p, 3] == 1];
a[n_] := EulerPhi[n]/3^b[n];
Table[a[n], {n, 1, 81}] (* Jean-François Alcover, Feb 17 2019 *)
PROG
(PARI) {b(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i]%3==1)};
{a(n)= eulerphi(n)/3^b(n)};
vector(80, n, a(n)) \\ G. C. Greubel, Feb 17 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Steven Finch, Mar 01 2006
EXTENSIONS
a(1)=1 prepended by Alois P. Heinz, Feb 17 2019
STATUS
approved