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

1,1

Links

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

Example

sopf(phi(203)) = sopf(168) = 12; phi(sopf(203)) = phi(36) = 12 hence 203 is a term of the sequence.

Mathematica

p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^4], p[EulerPhi[ # ]] == EulerPhi[ p[ # ]] &]

Prog

(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

Crossrefs

Cf. A008472, A075565, A075784, A075846, A076525, A076527, A076532, A076533.

Sequence in context: A229602 A080297 A080274 * A269552 A038789 A212997

Adjacent sequences: A076528 A076529 A076530 * A076532 A076533 A076534

Keyword

nonn

Author

Joseph L. Pe, Oct 18 2002

Extensions

Edited and extended by Ray Chandler, Feb 13 2005

Status

approved