cp's OEIS Frontend

A316786 Denominator of an upper bound for the maximal element in phi^(-1)(n).

%I A316786 #36 Feb 11 2021 21:24:07
%S A316786 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,
%T A316786 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,
%U A316786 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
%N A316786 Denominator of an upper bound for the maximal element in phi^(-1)(n).
%C A316786 A057635(n) <= A316785(n)/a(n).
%H A316786 Antti Karttunen, <a href="/A316786/b316786.txt">Table of n, a(n) for n = 1..5039</a>
%H A316786 R. Coleman, <a href="https://hal.archives-ouvertes.fr/hal-00718975">Some remarks on Euler's totient function</a>, HAL Id: hal-00718975, version 1, 2012.
%H A316786 H. Gupta, <a href="https://web.archive.org/web/20200728114321/http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a81_22.pdf">Euler's totient function and its inverse</a>, Indian J. Pure Appl. Math., 12(1) (1981), 22-29.
%H A316786 Antti Karttunen, <a href="/A316786/a316786.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A316786 Denominator of n*Product_{p prime, (p-1)|n} p/(p-1).
%e A316786 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.
%p A316786 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;
%o A316786 (PARI) a(n) = my(p=n); fordiv(n, d, if (isprime(d+1), p *= (d+1)/d)); denominator(p); \\ _Michel Marcus_, Jul 29 2018
%Y A316786 Cf. A057635, A316785 (numerators).
%K A316786 nonn,frac
%O A316786 1,12
%A A316786 _Franz Vrabec_, Jul 13 2018