A174568 Numbers n such that phi(n) + sigma(n) = sigma(n + phi(n)).

2, 3, 7, 19, 31, 37, 79, 97, 99, 135, 139, 157, 198, 199, 211, 229, 271, 287, 307, 331, 337, 350, 367, 379, 439, 499, 539, 547, 577, 601, 607, 619, 661, 671, 691, 727, 811, 829, 877, 923, 937, 967, 997, 1009, 1069, 1171, 1237, 1254, 1279, 1297, 1399, 1429

Offset: 1

Author

Michel Lagneau, Mar 22 2010

Keywords

• nonn

Comments

A005382 is included in this sequence : if p and 2p-1 primes, phi(p) = p-1, sigma(p)=p+1 and sigma(2p-1)=2p => phi(p) +sigma(p) = sigma(p+phi(p)). See the similar sequence A005384.

Examples

			2 is in the sequence because phi(2) + sigma(2) = 1 + 3 = 4, and sigma(2 + phi(2)) = sigma(3) = 4;
99 is in the sequence because phi(99) + sigma(99) = 60 + 156 = 216, and sigma(99 + phi(99)) = sigma(159) = 216.
		

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A005382, A005384, A057326, A057327, A057328, A057330, A005603.

Programs

Magma

[n: n in [1..1500] | (EulerPhi(n) + SumOfDivisors(n)) eq (SumOfDivisors(n + EulerPhi(n)))]; // Vincenzo Librandi, Jul 15 2015

Maple

with(numtheory):for n from 1 to 3000 do :if phi(n)+sigma(n) = sigma(n+phi(n)) then print(n):else fi:od:

Mathematica

Select[Range[1500],EulerPhi[#]+DivisorSigma[1,#]==DivisorSigma[1, #+ EulerPhi[ #]]&] (* Harvey P. Dale, Jul 05 2018 *)