A092586 Numbers k such that sigma(phi(k))-phi(sigma(k)) is nonzero and is divisible by (k+1), that is A065395(k)/(k+1) = (phi(sigma(k))-sigma(phi(k)))/(k+1) is a nonzero integer.
7, 87, 231, 463, 617, 691, 751, 855, 1059, 1127, 2795, 4819, 11999, 18527, 22481, 75311, 121939, 232901, 256751, 288883, 313919, 371519, 845831, 1285841, 1762799, 1815167, 7195199, 9096191, 40324121, 93070943, 99388823, 113140151, 238072223, 487394063
Offset: 1
Keywords
Examples
(sigma(phi(x))-phi(sigma(x)))/(x+1) equals 1 if x=7; is 2 if x=463; is 3 if x=4819.
Programs
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Mathematica
f[ x_] := EulerPhi[ DivisorSigma[1, x]] - DivisorSigma[1, EulerPhi[x]]; t = {}; Do[ s = f[n]; If[ s != 0 && Mod[ s, n + 1] == 0, Print[n]; AppendTo[t, n]], {n, 2*10^8}]; t
Extensions
Edited and extended by Robert G. Wilson v, Mar 03 2004
a(33)-a(34) from Donovan Johnson, Mar 04 2013