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A316786 Denominator of an upper bound for the maximal element in phi^(-1)(n). 2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 4, 1, 1, 1, 4, 1, 20, 1, 2, 1, 1, 1, 1728, 1, 1, 1, 8, 1, 2, 1, 2, 1, 1, 1, 32, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 5760, 1, 1, 1, 1, 1, 44, 1, 1, 1, 10, 1, 62208, 1, 1, 1, 1, 1, 2, 1, 64, 1, 1, 1, 192, 1, 1, 1, 88, 1, 120, 1, 2, 1, 1, 1, 1536, 1, 1, 1, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,12
COMMENTS
A057635(n) <= A316785(n)/a(n).
LINKS
R. Coleman, Some remarks on Euler's totient function, HAL Id: hal-00718975, version 1, 2012.
H. Gupta, Euler's totient function and its inverse, Indian J. Pure Appl. Math., 12(1) (1981), 22-29.
FORMULA
Denominator of n*Product_{p prime, (p-1)|n} p/(p-1).
EXAMPLE
For n = 12, there are 5 primes p with (p-1)|12: p1 = 2, p2 = 3, p3 = 5, p4 = 7, and p5 = 13. The denominator of 12*(2/1)*(3/2)*(5/4)*(7/6)*(13/12) = 455/8 is a(12) = 8.
MAPLE
with(numtheory): A316786 := proc(n) local d, N; N:=n; for d in divisors(n) do if is prime(d+1) then N := (N*(d+1))/(d) end if; end do; denom(N); end proc;
PROG
(PARI) a(n) = my(p=n); fordiv(n, d, if (isprime(d+1), p *= (d+1)/d)); denominator(p); \\ Michel Marcus, Jul 29 2018
CROSSREFS
Cf. A057635, A316785 (numerators).
Sequence in context: A284098 A010152 A327155 * A011264 A276405 A066341
KEYWORD
nonn,frac
AUTHOR
Franz Vrabec, Jul 13 2018
STATUS
approved

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Last modified March 28 08:02 EDT 2024. Contains 371236 sequences. (Running on oeis4.)