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A076533
Numbers n such that sum of the distinct prime factors of phi(n) = sum of the distinct prime factors of sigma(n).
10
1, 3, 14, 35, 42, 70, 105, 119, 209, 210, 238, 248, 297, 357, 412, 418, 477, 594, 595, 616, 627, 714, 744, 954, 1045, 1142, 1178, 1190, 1236, 1240, 1254, 1328, 1339, 1463, 1485, 1672, 1674, 1703, 1736, 1785, 1848, 1863, 2079, 2090, 2376, 2385, 2540, 2728
OFFSET
1,2
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
sopf(sigma(14)) = 5; sopf(phi(14)) = 5; hence 14 is a term of the sequence.
MATHEMATICA
p[n_] := Apply[Plus, Transpose[FactorInteger[n]][[1]]]; Select[Range[3, 10^4], p[DivisorSigma[1, # ]] == p[EulerPhi[ # ]] &]
Select[Range[3000], Total[FactorInteger[DivisorSigma[1, #]][[All, 1]]] == Total[ FactorInteger[EulerPhi[#]][[All, 1]]]&] (* Harvey P. Dale, Sep 20 2016 *)
PROG
(PARI) sopf(n)=my(f=factor(n)[, 1]); sum(i=1, #f, f[i])
is(n)=sopf(sigma(n))==sopf(eulerphi(n)) \\ Charles R Greathouse IV, Mar 09 2014
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Oct 18 2002
EXTENSIONS
Edited by Ray Chandler, Feb 13 2005
a(1) inserted by Charles R Greathouse IV, Mar 09 2014
STATUS
approved