A333338 Numbers k such that sigma_2(k) = sigma_2(phi(k)).

1, 7, 11891, 130801, 273493, 1438811, 3008423, 6290339, 15826921, 33092653, 69193729, 144677797, 174096131, 364019183, 761131019, 1591455767, 1915057441, 3327589331, 4004211013, 8372441209, 17506013437, 21065631851, 36603482641, 44046321143, 76534554613, 92096853299

Offset: 1

Author

Ivan N. Ianakiev, Mar 14 2020

Keywords

• nonn

Comments

The sequence is infinite since it contains all the numbers of the form 11^i*23^j*47 for i,j > 0. Up to 10^11 the only terms not of this form are 1 and 7. - Giovanni Resta, Mar 15 2020

Examples

			50 = 1^2 + 7^2 (sum of the squares of the divisors of 7) = 1^2 + 2^2 + 3^2 + 6^2 (sum of the squares of the divisors of 6 = phi(7)). So 7 is in the sequence.
		

Crossrefs

Cf. A000010, A001157, A070418, A033631.

Programs

Mathematica

Select[Range[10!],DivisorSigma[2,#]==DivisorSigma[2,EulerPhi[#]]&]

PARI

isok(m) = sigma(m, 2) == sigma(eulerphi(m), 2); \\ Michel Marcus, Mar 15 2020

Extensions

More terms from Giovanni Resta, Mar 15 2020