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A364932
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a(n) = phi(psi(n)).
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1
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1, 2, 2, 2, 2, 4, 4, 4, 4, 6, 4, 8, 6, 8, 8, 8, 6, 12, 8, 12, 16, 12, 8, 16, 8, 12, 12, 16, 8, 24, 16, 16, 16, 18, 16, 24, 18, 16, 24, 24, 12, 32, 20, 24, 24, 24, 16, 32, 24, 24, 24, 24, 18, 36, 24, 32, 32, 24, 16, 48, 30, 32, 32, 32, 24, 48, 32, 36, 32, 48, 24
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OFFSET
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1,2
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COMMENTS
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Here phi is Euler's totient function and psi is the Dedekind psi function.
Values of psi(n), n > 1 are always greater than n, while values of phi(n), n > 1 are always less than n.
a(39270) = 41472 is the first term where phi(psi(n)) exceeds n.
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LINKS
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FORMULA
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MAPLE
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f:= proc(n) local p; numtheory:-phi(n * mul(1+1/p, p = numtheory:-factorset(n))) end proc:
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MATHEMATICA
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a[n_] := EulerPhi[n*Times @@ (1 + 1/FactorInteger[n][[;; , 1]])]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Aug 13 2023 *)
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PROG
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(Python)
from sympy.ntheory.factor_ import totient
from sympy import isprime, primefactors, prod
def psi(n):
plist = primefactors(n)
return n*prod(p+1 for p in plist)//prod(plist)
def a(n): return totient(psi(n))
(PARI) a(n) = eulerphi(n * sumdivmult(n, d, issquarefree(d)/d)); \\ Michel Marcus, Aug 13 2023
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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