A076531 Numbers n such that sopf(phi(n)) = phi(sopf(n)), where sopf(x) = sum of the distinct prime factors of x.
3, 203, 322, 377, 644, 851, 931, 1166, 1211, 1288, 1421, 1666, 1815, 1862, 2332, 2576, 3332, 3724, 4664, 4830, 5152, 6401, 6517, 6664, 7042, 7241, 7448, 9075, 9328, 9555, 9660, 9845, 9922, 9947, 10304, 10465, 11662, 11814, 11830, 12558, 12903, 13034
Offset: 1
Keywords
Examples
sopf(phi(203)) = sopf(168) = 12; phi(sopf(203)) = phi(36) = 12 hence 203 is a term of the sequence.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^4], p[EulerPhi[ # ]] == EulerPhi[ p[ # ]] &]
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PARI
sopf(n) = my(f=factor(n)); sum(j=1, #f~, f[j, 1]); \\ A008472 isok(n) = eulerphi(sopf(n)) == sopf(eulerphi(n)); \\ Michel Marcus, Oct 04 2019
Extensions
Edited and extended by Ray Chandler, Feb 13 2005