A137817 Cubeful "year numbers" (such that phi(n) = 2 phi(sigma(n)): A137815).

295569, 295947, 1586763, 1811079, 1964375, 2069469, 4473387, 5854375, 6820555, 7285923, 10936053, 12233457, 13260625, 18029709, 18052767, 21153663, 21576537, 21604131, 22182093, 22877451, 23744043, 25536875, 28340307, 34102775

Offset: 1

Author

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

Keywords

• nonn

Comments

See A137815 for general comments and references about "year numbers". This is the subsequence of cubeful elements of A137815, i.e. its intersection with A046099. As such, it is of course also a subsequence of A137816.

There are only 56 such numbers below 10^8.

Links

• M. F. Hasler and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 56 terms from _M. F. Hasler_)

Crossrefs

Cf. A137815-A137819, A006872. A046099. A067704.

Programs

PARI

for( i=1,#A137816, vecmax( factor( A137816[i] )[,2])>2 && print1(A137816[i]", "))

PARI

for( i=1,#A046099, eulerphi(A046099[i])==2*eulerphi(sigma(A046099[i])) && print1( A046099[i] ", "))

PARI

for( n=1,10^9, issquarefree(n) && next; vecmax(factor(n)[,2])>2 || next; eulerphi(n)==2*eulerphi(sigma(n)) && print1(n", "))