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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

(sigma(phi(x))-phi(sigma(x)))/sigma(x) quotient equals 1 for x=7, 2 for x=327, 3 for x=5609.

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

Prog

(PARI) is(n)=my(s=sigma(n), t=sigma(eulerphi(n))-eulerphi(s)); t && t%s==0 \\ Charles R Greathouse IV, Feb 14 2013

Crossrefs

Cf. A000010, A000203, A033632, A065395, A092584-A092588.

Sequence in context: A163437 A109059 A002000 * A049686 A177019 A160432

Adjacent sequences: A092585 A092586 A092587 * A092589 A092590 A092591

Keyword

nonn

Author

Labos Elemer, Mar 01 2004

Status

approved