A076533 Numbers n such that sum of the distinct prime factors of phi(n) = sum of the distinct prime factors of sigma(n).

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

Crossrefs

Cf. A008472, A075565, A075784, A075846, A076525, A076527, A076531, A076532.

Sequence in context: A077288 A094627 A009394 * A081379 A081377 A050934

Adjacent sequences: A076530 A076531 A076532 * A076534 A076535 A076536

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