A137816 Nonsquarefree "year numbers" (numbers n such that phi(n) = 2*phi(sigma(n)): A137815).

5491, 8075, 25317, 27455, 71383, 72283, 76131, 104975, 138575, 193041, 203167, 295569, 295947, 298775, 334951, 356915, 361415, 400843, 451535, 492275, 509575, 572975, 589475, 595975, 654493, 683757, 815975, 862087, 876627, 919075, 936729

Offset: 1

Author

R. K. Guy, R. J. Mathar and M. F. Hasler, Feb 11 2008

Keywords

• nonn

Comments

This is the subsequence of nonsquarefree elements of A137815. See there for more comments and references.

There are only 32 such numbers below 10^6, 145 below 10^7 and 785 below 10^8.

Links

• M. F. Hasler, Table of n, a(n) for n=1,...,785.

Crossrefs

Cf. A137815-A137819, A006872, A067704.

Programs

Mathematica

Reap[For[n=1, n<10^6, n++, If[!SquareFreeQ[n] && EulerPhi[n] == 2*EulerPhi[ DivisorSigma[1, n]], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Dec 12 2016 *)

PARI

for( n=1,10^6, !issquarefree(n) && eulerphi(n)==2*eulerphi(sigma(n)) && print1(n", "))