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

1,1

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.

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].

Example

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.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A354215 A334050 A073640 * A005382 A195354 A244638

Adjacent sequences: A174565 A174566 A174567 * A174569 A174570 A174571

Keyword

nonn

Author

Michel Lagneau, Mar 22 2010

Status

approved