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A072911
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Number of "phi-divisors" of n.
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1
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1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 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, 2, 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, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| If n = Product p(i)^r(i), d = Product p(i)^s(i), = s(i)<=r(i) and GCD(s(i),r(i))=1, then d is a phi-divisor of n.
The integers n=prod_{i=1}^r p_i^{a_i} and m=prod_{i=1}^r p_i^{b_i}, a_i,b_i>=1 (1<=i<=r) having the same prime factors are called exponentially coprime, if gcd (a_i,b_i)=1 for every 1<=i<=r, i.e. the only common exponential divisor of n and m is prod_{i=1}^r p_i = the common squarefree kernel of n and m, cf. A049419, A007947. The terms of this sequence count the number of divisors d of n such that d and n are exponentially coprime. [From Laszlo Toth (ltoth(AT)ttk.pte.hu), Oct 06 2008]
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REFERENCES
| J. Sandor, On an exponential totient function, Sudia Univ. Babes-Bolyai, Math., 41 (1996), 91-94. [From Laszlo Toth (ltoth(AT)ttk.pte.hu), Oct 06 2008]
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LINKS
| L. Toth, On certain arithmetic functions involving exponential divisors, Annales Univ. Sci. Budapest., Sect. Comp., 27 (2004), 285-294. [From Laszlo Toth (ltoth(AT)ttk.pte.hu), Oct 06 2008]
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FORMULA
| If n = Product p(i)^r(i) then a(n) = Product (phi(r(i))), where phi(k) is the Euler totient function of k, cf. A000010.
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MAPLE
| A000010 := proc(n) numtheory[phi](n) ; end: A072911 := proc(n) local ifs, a, p; a := 1 ; ifs := ifactors(n)[2] ; for p in ifs do a := a*A000010(op(2, p)) ; od: RETURN(a) ; end: for n from 1 to 150 do printf("%d, ", A072911(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 25 2008]
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CROSSREFS
| Cf. A061389.
Sequence in context: A043281 A061704 A050361 * A053150 A163379 A006466
Adjacent sequences: A072908 A072909 A072910 * A072912 A072913 A072914
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KEYWORD
| nonn,mult
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AUTHOR
| Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Aug 21, 2002.
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 25 2008
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