A092588 Numbers k such that sigma(phi(k)) - phi(sigma(k)) is nonzero and divisible by sigma(k), that is A065395(k)/A000203(k) is a nonzero integer.
7, 327, 463, 497, 617, 691, 751, 1207, 1633, 2451, 2643, 3143, 3337, 3503, 4939, 5609, 7093, 7597, 10327, 14987, 20427, 21103, 22345, 22481, 24739, 26491, 27193, 28077, 37753, 37915, 42711, 42717, 47647, 48043, 49243, 50071, 51727, 54823, 57478
Offset: 1
Keywords
Examples
(sigma(phi(x))-phi(sigma(x)))/sigma(x) quotient equals 1 for x=7, 2 for x=327, 3 for x=5609.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
fs[x_] := EulerPhi[DivisorSigma[1, x]] sf[x_] := DivisorSigma[1, EulerPhi[x]] {t=Table[0, {100}], j=1}; Do[s=(sf[n]-fs[n])/DivisorSigma[1, n]; If[ !Equal[s, 0]&&IntegerQ[s], Print[n];t[[j]]=n;j=j+1], {n, 2, 1000000}] t -
PARI
is(n)=my(s=sigma(n),t=sigma(eulerphi(n))-eulerphi(s)); t && t%s==0 \\ Charles R Greathouse IV, Feb 14 2013