A073477 Least k such that 2^n = k^2-sigma(k)*phi(k).

2, 4, 8, 16, 32, 12, 20, 256, 44, 1024, 2048, 4096, 8192, 16384, 992, 65536, 724, 262144, 2080, 1048576, 16256, 4194304, 8388608, 16777216, 33554432, 67108864, 48832, 268435456, 536870912, 1073741824, 471808, 4294967296, 8589934592, 17179869184, 34359738368

Offset: 0

Author

Benoit Cloitre, Aug 26 2002

Keywords

• nonn
• changed

Comments

Sequence is always defined since for s=2^(n+1), 2^n = s^2-sigma(s)*phi(s). - R. J. Mathar, Oct 01 2011

a(38) = 67100672. a(50) = 17179738112. a(56) <= 274877382656. - Donovan Johnson, Oct 02 2011

Programs

PARI

a(n)=if(n<0,0,x=1; while(abs(x^2-sigma(x)*eulerphi(x)-2^n)>0,x++)); x

Formula

a(n) = min{k: A069249(k)=2^n}. - R. J. Mathar, Oct 01 2011

Extensions

Edited and extended by Klaus Brockhaus, Aug 29 2002

a(26) and a(30) from R. J. Mathar, Oct 01 2011

a(25), a(27)-a(29) and a(31)-a(34) from Donovan Johnson, Oct 02 2011