proposed

approved

editing

proposed

nn=10^4; lim=Floor[Sqrt[nn]]; mx=Table[0, {lim}]; Do[c=n-EulerPhi[n]; If[0<c<=lim, mx[[c]]=n], {n, nn}]; Rest[mx] (* _T. D. Noe_ *)

Table[Module[{k = n^2}, While[And[k - EulerPhi@ k != n, k > 0], k--];

k], {n, 2, 62}] (* Michael De Vlieger, Mar 17 2017 *)

approved

editing

_Labos E. (labos(AT)ana.sote.hu), Elemer_, Aug 13 2001

Corrected and edited by _T. D. Noe (noe(AT)sspectra.com), _, Oct 30 2006

T. D. Noe, <a href="/A063748/b063748.txt">Table of n, a(n) for n=2..1000</a>

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T. D. Noe, <a href="http://www.research.att.com/~njas/sequences/b063748.txt">Table of n, a(n) for n=2..1000</a>

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nn=10^4; lim=Floor[Sqrt[nn]]; mx=Table[0, {lim}]; Do[c=n-EulerPhi[n]; If[0<c<=lim, mx[[c]]=n], {n, nn}]; Rest[mx] (Tony T. D. Noe)

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Inverse cototientGreatest x that is a solution to x-phi(A051853x) sets represented by their largest term =n or by 0 zero if set there is no solution, where phi(x) is emptyEuler's totient function.

4, 9, 8, 25, 10, 49, 16, 27, 0, 121, 22, 169, 26, 55, 32, 289, 34, 361, 38, 85, 30, 529, 46, 133, 0, 187, 52, 841, 58, 961, 64, 253, 0, 323, 68, 1369, 74, 391, 76, 1681, 82, 1849, 86, 493, 70, 2209, 94, 589, 0, 667, 0, 2809, 106, 703, 104, 697, 0, 3481, 118, 3721, 122

See A051953 for x-phi(x), the cototient function. Note that a(n)=0 for n in A005278. Also note that n=1 has an infinite number of solutions. If n is prime, then a(n)=n^2. If n is even, then a(n)<=2n. In particular, if n=p+1 for a prime p, then a(n)=2n-2. Also, if n=2^k, then a(n)=2n. If n>9 is odd and composite, then a(n)=pq, with p>q odd primes with p+q=n+1 and p-q minimal. We can take p=A078496((n+1)/2) and q=A078587((n+1)/2).

T. D. Noe, <a href="http://www.research.att.com/~njas/sequences/b063748.txt">Table of n, a(n) for n=2..1000</a>

For m = 1, InvCot[1] = {primes} so no max term exists. For m = nonprime m-Phi[m]>= Sqrt[m] so Max{Cototient[m]} <= m^2. If m = prime, then Max{InvCototient[p]} = p^2. m = 23, InvCototient(23) = {95,119,143,529},a(29) = 529. m = 24, InvCototient(24) = {36,40,44,46},a(24) = 46.

For n=15, the solutions are x=39 and x=55, so a(15)=55. Note that 55=5*11 and 5+11=n+1.

nn=10^4; lim=Floor[Sqrt[nn]]; mx=Table[0, {lim}]; Do[c=n-EulerPhi[n]; If[0<c<=lim, mx[[c]]=n], {n, nn}]; Rest[mx] (Tony Noe)

Cf. A000010, A051953, A063507.

Cf. A063507 (least solution to x-phi(x)=n), A063740 (number of solutions to x-phi(x)=n).

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Corrected and edited by T. D. Noe (noe(AT)sspectra.com), Oct 30 2006

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Labos E. (labos(AT)ana1ana.sote.hu), Aug 13 2001