

A230237


Numbers n such that phi(n) + sigma(n) is the mean value of phi(sigma(n)) and sigma(phi(n)).


2



46427, 66929, 1560793, 1796647, 1810601, 1839673, 2053781, 2176673, 2426063, 2467007, 3172013, 3898603, 4208939, 12011921, 19504309, 29241797, 35464241, 35501573, 46838431, 46976227, 66580381, 69406561, 88015273, 104722321
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OFFSET

1,1


COMMENTS

All terms below 110000000 are odd and squarefree. What is the smallest term of other form?
a(28) = 233187611 = 31^2 * 167 * 1453 is the first nonsquarefree term.  Charles R Greathouse IV, Oct 17 2013


LINKS

Charles R Greathouse IV and Donovan Johnson, Table of n, a(n) for n = 1..119 (terms < 3*10^10, first 88 terms from Charles R Greathouse IV)


MATHEMATICA

Do[If[2(DivisorSigma[1, n]+EulerPhi[n])==EulerPhi[DivisorSigma[1, n]]+DivisorSigma[1, EulerPhi[n]], Print[n]], {n, 110000000}]
Select[Range[1048*10^5], EulerPhi[#]+DivisorSigma[1, #]==Mean[{EulerPhi[ DivisorSigma[ 1, #]], DivisorSigma[ 1, EulerPhi[ #]]}]&] (* Harvey P. Dale, Jan 16 2020 *)


PROG

(PARI) for(n=1, 1e8, f=factor(n); ph=eulerphi(f); s=sigma(f); if(2*ph+2*s == sigma(ph)+eulerphi(s), print1(n", "))) \\ Charles R Greathouse IV, Oct 17 2013


CROSSREFS

Cf. A000010, A000203, A062401, A062402, A230238.
Sequence in context: A251278 A202897 A185518 * A175170 A204495 A157527
Adjacent sequences: A230234 A230235 A230236 * A230238 A230239 A230240


KEYWORD

nonn


AUTHOR

Farideh Firoozbakht, Oct 16 2013


STATUS

approved



