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 A174568 Numbers n such that phi(n) + sigma(n) = sigma(n + phi(n)) 1
 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 (list; graph; refs; listen; history; text; internal format)
 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, 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: A214627 A334050 A073640 * A005382 A195354 A244638 Adjacent sequences:  A174565 A174566 A174567 * A174569 A174570 A174571 KEYWORD nonn AUTHOR Michel Lagneau, Mar 22 2010 STATUS approved

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Last modified October 16 19:13 EDT 2021. Contains 348043 sequences. (Running on oeis4.)