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A321167 The e-unitary Euler function: a(1) = 1, a(n) = Product uphi(e(i)) for n = Product p(i)^e(i), where uphi is the unitary totient function (A047994). 0
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

The unitary version of A072911.

For n = Product p(i)^e(i) > 1, a(n) is the number of divisors d of n such that d and n are exponentially unitary coprime, i.e., d = Product p(i)^f(i) where 1 <= f(i) <= e(i) and uGCD(f(i), e(i)) = 1 for any any i, where uGCD(m, n) is the largest divisor of m that is a unitary divisor of n.

LINKS

Table of n, a(n) for n=1..87.

Nicusor Minculete and László Tóth, Exponential unitary divisors, Annales Univ. Sci. Budapest., Sect. Comp. Vol. 35 (2011), pp. 205-216.

MATHEMATICA

f[p_, e_] := p^e-1; uphi[1] = 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; fe[p_, e_] := uphi[e]; euphi[n_] := Times @@ fe @@@ FactorInteger[n]; Array[euphi, 100]

CROSSREFS

Cf. A047994, A072911.

Sequence in context: A204127 A225174 A059895 * A190867 A117358 A294333

Adjacent sequences:  A321164 A321165 A321166 * A321168 A321169 A321170

KEYWORD

nonn,mult

AUTHOR

Amiram Eldar, Jan 10 2019

STATUS

approved

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Last modified March 22 03:08 EDT 2019. Contains 321406 sequences. (Running on oeis4.)