A137818 Non-biquadratefree "year numbers": phi(n) = 2 phi(sigma(n)) and p^4 | n for some p>1.

295569, 1811079, 1964375, 2069469, 4473387, 5854375, 10936053, 13260625, 18029709, 21576537, 22182093, 25536875, 35595625, 46404333, 49648383, 55094375, 57044817, 58650625, 67009923, 69166467, 72681875, 76106875

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 elements of A137815 divisible by a biquadrateful number, i.e. its intersection with A046101 (numbers divisible by the 4th power of some prime). As such, it is of course also a subsequence of A137817 and a fortiori of A137816.

There are only 28 such numbers below 10^8.

Links

• Donovan Johnson, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A137815-A137819, A046101.

Programs

PARI

for( i=1,#A137816, vecmax( factor( A137816[i])[,2])>3 && 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])>3 || next; eulerphi(n)==2*eulerphi(sigma(n)) && print1(n", "))